Kapitza Institute for Physical Problems, Moscow, Last Seminars

1. U. Gavish
   (LKB, Ecole Normale Superieure, Paris)

   HEISENBERG CONSTRAINTS ON MESOSCOPIC AND MOLECULAR AMPLIFIERS

   The Heisenberg principle puts constraints on the performances of linear amplifiers. We derive these constraints for the case of molecular or mesoscopic amplifiers with a narrow-band input. We then explain what physical processes create the noise which is necessarily added to the signal in order to satisfy these constraints. Finally we specify ways to minimize this noise.

1. S.N. Molotkov (ISSP)

   SOME ASPECTS OF PRACTICAL QUANTUM CRYPTOGRAPHY

   No annotation presented.

1. Peter Hirschfeld (University of Florida)

   NANOSCALE INHOMOGENEITIES AND SPECTROSCOPIES ON BSCCO-2212

   In almost all high-temperature superconducting cuprate materials, doping naturally introduces disorder. Recent STM experiments have provided us with a remarkable window on the real space electronic structures which reflect this disorder, and found localized atomic scale resonances, nanoscale gap inhomogeneity, and long-range spatial modulations with well-defined wave vectors. I discuss to what extent these results can be understood in terms of BCS d-wave quasiparticle states interfering in the presence of many potential scatterers, and present both analytical results as well as numerical solutions of the Bogoliubov-de Gennes equations on 120x120 lattices. I further propose a ``realistic" model for the disorder, involving in-plane unitary scatterers and a smooth weak disorder component, which seems to work well for BSCCO-2212 but should be quite nonuniversal. Remaining discrepancies may point to novel physics such as correlation-induced magnetic moments, or coexistence with anomalous subdominant order. Implications for transport properties and angle-resolved photoemission using this model are also discussed.

1. A.A. Starobinsky

   DETERMINING PROPERTIES OF DARK ENERGY IN THE UNIVERSE

   Recent numerous observational data obtained from such independent sources as angular anisotropies of the cosmic microwave background radiation, large-scale gravitational clustering of galaxies and their clusters and observations of supernovae explosions at high redshifts prove convincingly that about 70% of the total energy density of matter in the present Universe is due to a new kind of matter in the Universe ("dark energy") which is non-baryonic, has negative pressure which modulus is very close to dark energy density (if the Einsteinian form of gravity field equations is assumed) and remains unclustered at all scales where the clustering of baryons and dust-like cold dark matter is seen. I discuss different forms of phenomenological description of dark energy properties, present limits on variation of dark energy density with redshift which follow from the most recent supernovae data and make a brief review of different theoretical models of dark energy including those in which it has a purely geometrical origin. The simplest possibility of dark energy being a cosmological constant and nothing more still remains a good fit to all existing observational data. However, more complicated behaviour including breaking of the weak energy condition for dark energy for redshifts z < 0.5 combined with some increase of its energy density with redshift for larger z is possible, too.

1. V. V. Ryazanov (ISSP)

   CRITICAL CURRENTS AND CURRENT-PHASE RELATION OF SFS JOSEPHSON JUNCTIONS

   We have investigated experimentally the pi-state of Josephson SFS (superconductor-ferromagnet-superconductor) junctions. The origin of the pi-state is an oscillating and sign-reversal superconducting order parameter induced in the ferromagnet close to the SF-interface. Transition to the pi-state occurs for ferromagnetic interlayer thickness close to a half-period of the order parameter spatial oscillations. We have also observed back transition to conventional "0-state" at the F-layer thickness about of the period of the oscillations. Weak ferromagnetism of the F-layer (Cu/Ni alloy) allows us to fabricate thin-film Josephson SFS sandwiches with continuous homogeneous interlayers whose thickness (10-30 nm) is comparable with the pair-decay length in the ferromagnet and to observe a temperature 0-pi-transitions. We present also measurements of the current-phase relation (CPR) of SFS Josephson junctions as a function of temperature. The CPR is determined by incorporating the junction in a superconducting loop coupled to a dc SQUID, allowing measurement of the junction phase difference.

1. M. V. Feigel'man, A. S. Ioselevich, M. A. Skvortsov

   QUANTUM PERCOLATION IN GRANULAR METALS

   Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages suppress mean conductance much stronger than its variance. At sufficiently low energies any distribution becomes broad, leading to strong local fluctuations of tunneling density of states. Percolative nature of metal-insulator transition is established by combination of analytic and numerical analysis of matrix renormalization group equations.

1. Yu. S. Barash (ISSP)

   ANDREEV STATES NEAR SURFACES AND IN THIN FILMS OF HIGH-TEMPERATURE SUPERCONDUCTORS

   Investigations of Andreev bound states in high-temperature superconductors will be shortly described in the Introduction. In the second and the third parts of the talk, new results of two papers will be represented.

   Effects of impurities, situated on (110) surface of d-wave superconductor, will be considered regarding the low-bias conductance of tunnel NIS junctions. Impurity-induced quasiparticle bound states on a pair-breaking surface of a d-wave superconductor are theoretically described, taking into account hybridization of impurity- and surface-induced Andreev states. Further, a theory for effects of surface disorder (of thin impurity surface layer) on the low-bias conductance of tunnel junctions is developed. In the third part of the talk we present analytical and numerical results for the electronic spectra of thin films (quantum wires) of a d-wave superconductor on a square lattice. The spectra of Andreev and other quasiparticle states, as well as the spatial and particle-hole structures of their wave functions, depend on interference effects caused by the presence of the surfaces and are qualitatively different for half-filled wires with even or odd number of chains. Effects of deviations from half-filling and results of the self-consistent calculations are also presented.

1. Dmitry Gorbunov (INR RAS)

   PUZZLES OF ULTRA-HIGH -- ENERGY COSMIC RAYS (UHECRS)

   Traveling in intergalactic medium protons of E>5*10¹⁹ eV start to lose energy rapidly due to pion production on cosmic microwave background (CMB) photons. Thus at higher energies only protons from local sources can reach the Earth. At lower energies protons cover a very large distance almost without attenuation. Based on this simple considerations the cut off in UHECRs spectrum has been predicted, that conflicts with experimental data. Although the statistic of anomalous events is low, one can try to provide an explanation for the observed behavior of the UHECR spectra. All attempts within the Standard Model of particle physics are failed. Therefore, possibly, UHECRs provide one of the few direct experimental evidences for the physics beyond the Standard Model. We are about to review the current status of the problems related to the absence of the cut off in UHECRs spectrum.

1. Tatyana I. Baturina
   (Insitut fiziki poluprovodnikov, Novosibirsk)

   COHERENT PHENOMENA IN MULTIPLY CONNECTED SNS SYSTEMS

   Mesoscopic systems, consisting of a normal metal (N) or heavily doped semiconductor being in contact with a superconductor (S), have lately received much attention mainly because of a big variety of associated quantum effects. The key mechanism governing the carrier transport through the NS contact is the Andreev reflection. When a normal metal is placed between two superconducting electrodes another mechanism is involved in the charge transfer. It is the multiple Andreev reflection process (MAR). These phenomena result in nonlinear current-voltage characteristics, which exhibit an anomalous resistance dip at zero bias, the subharmonic energy gap structure, etc.

   Although at present the properties of single SNS junctions are well studied both theoretically and experimentally, the effect of the Andreev reflection and MAR process on the properties of a system consisting of a large number of normal metal regions connected by superconducting islands is practically not investigated. I will present the results of low-temperature transport measurements on two-dimensional arrays, on chains of SNS junctions and on single SNS junctions fabricated on the basis of superconducting PtSi film and perform a comparative analysis of their properties.

   Some unexpected coherence effects are found in multiply connected SNS systems, namely:

   (i) the gradual decrease of the effective suppression voltage for the excess conductivity observed at zero bias as the quantity of the SNS junctions increases, (ii) the strengthening of subharmonic energy gap structure in two-dimensional arrays of SNS junctions, (iii) a rich fine structure in the dV/dI-V dependences at dc bias voltages higher than the superconducting gap and corresponding to some multiples of 2Δ/e in chains of SNS junctions.

   All these results show that coherent phenomena governed by the Andreev reflection are not only maintained over the macroscopic scale but manifest novel pronounced effects as well.

   
   I will discuss some possible approaches to explain the observed phenomena.

1. A. Pukhov, S. Gordienko

   RELATIVISTIC DOPPLER EFFECT: UNIVERSAL SPECTRA AND ZEPTOSECOND PULSES

   For the first time we report on a numerical observation of the train of zeptosecond pulses produced by reflection of a relativistically intense femtosecond laser pulse from the oscillating boundary of an overdense plasma because of the Doppler effect. These pulses promise to become a unique experimental and technological tool since their length is of order of the Bohr radius and the intensity is extremely high ~10¹⁹ W/cm2. We present the physical mechanism, analytical theory, and direct particle-in-cell simulations. We show that the harmonic spectrum is universal: the intensity of the n-th harmonic scales as 1/n³ for n < 4γ², where γ is the largest γ-factor of the electron fluid boundary. The subattosecond pulses originate from this universal spectrum.

1. Michael Praehofer

   BORDER LEDGE FLUCTUATIONS OF CRYSTAL FACETS

   Crystals in equilibrium consist of facets connected by rounded surfaces. On atomic scale the facet is surrounded by step lines or ledges whose density vanishes. There fluctuations are entropically reduced with respect to a single meandering ledge. We develop a scaling theory for the fluctuations and connect the statistics of the last ledge to the eigenvalue statistics of random matrices.

1. K. Nagaev

   SEMICLASSICAL STATISTICS OF NOISE IN MESOSCOPIC SYSTEMS

   A brief overview of the traditional Full Counting Statistics in mesoscopic systems will be given and principles of recently proposed semiclassical statistics of noise will be formulated. Special emphasis will be put on the frequency dependence of higher cumulants of noise.

1. V.N. Ryzhov (HPPI)

   CLUSTER MODEL OF LOCAL STRUCTURE AND BOND ORIENTATIONAL ORDER IN LENNARD-JONES LIQUID

   While the experimental and phenomenological knowledge of non-ergodic amorphous phases has been considerably improved in the last time, progress in the first-principle statistical mechanical studies of physical properties of supercooled liquids and glasses is much more slow. In this talk we discuss the microscopic approach to the study of the local structure and possible phase transitions in supercooled liquids based on the generalization of the density functional theory in classical statistical mechanics. A concept of the bond orientational order in simple liquids in two and three dimensions is reviewed, and the model of interacting cubic and icosahedral clusters in the Lennard-Jones liquid is proposed. In the framework of the model the analog of spin glass quenched disorder appears in a natural way in the Lennard-Jones system. The model is solved in the mean-field replica symmetric approximation. It is shown that the bond orientational order grows smoothly upon cooling, the symmetry of the ordered state being mainly cubic. The temperature of the possible glass transition is identified with the temperature at which the replica symmetry is broken.

1. S.E. Korshunov

   ORDERED STATES AND PHASE TRANSITIONS IN TWO-DIMENSIONAL FRUSTRATED XY-MODELS

   1. Frustrated XY-models and their application.
   2. Coulomb gas representation.
   3. Ordered states and phase transitions at small frustration (f<<1).
   4. The fully frustrated model (f=1/2)
   with square or triangular lattice:
   
   a) fractional vortices;
   b) kink pairs unbinding on a domain wall and its consequences
   for the sequence of phase transitions in the "bulk";
   c) addition of further neighbors.
   
   5. Ordered states in the vicinity of f=1/2.
   6. Zero-energy domain walls. Removal of accidental degeneracy
   by fluctuations (a few examples).

1. V. Dotsenko

   MEAN-FIELD REPLICA APPROACH FOR LIQUID-GLASS PHASE TRANSITION

   In this talk we discuss recently developed statistical mechanical ideas for structural glasses. In particular we focus onto the first principle and mean-field computations for simple models of glasses with the two-body interparticle potentials. It is argued that on a qualitative level the equilibrium thermodynamics of the low-temperature glassy phase, as well as the liquid-glass phase transitions, can be described using the methods developed in the replica theory of spin-glasses and others disordered systems.

1. A.Yu. Dem'yanov, N.A.Inogamov, A.M. Oparin

   BUBBLE MOTION IN INCLINED PIPES

   We analyze strongly nonlinear fluid motion with free surface in vertical, inclined, and horizontal pipes. The problem concerning rise of buoyant bubbles in vertical pipes is closely connected to the problem of Rayleigh-Taylor instability (instability of hydrostatic equilibrium when heavy fluid is imposed above light one). Inclined pipes are intensively investigated in connection with problems of transportation of gas-liquid or liquid-liquid flows. We develop a new approach to the problem of motion of large bubbles in wide pipes (large and wide mean that capillary scale is small). As against the previous approaches based on semiempirical methods, in the given work the analytical methods concerning the theory of potential are used. We do careful comparison of obtained solutions for two and three-dimensional spaces. It is shown that not always increase of dimension leads to an increase in velocity of rise of bubbles (as it is usually supposed). For the first time direct numerical simulations (DNS) are applied for studies of flows with free boundary in inclined pipes. We also use them in our work. They allow us, first, to check up accuracy of our analytical models and, second, to obtain the general picture of motion.

1. Igor Erukhimovich

   (Condensed matter theory group, Institute of Physics, Johannes-Gutenberg-University of Mainz, Germany and A.N. Nesmeyanov Institute of Organoelement Compounds RAS, Moscow, Russia)

   WEAK CRYSTALLIZATION IN POLYMER SYSTEMS

   In this talk we review the current state of the theoretical and experimental results on polymer systems capable to undergo weak crystallization phase transition and present some of our new results in this field. The following issues will be addressed:

   1. What are the block copolymers, polyelectrolytes, random and randomly correlated copolymers and why are they expected to undergo weak crystallization.

   2. The basic idea of the Leibler microscopic theory of weak crystallization in block copolymers: relationship between the vertices of the phenomenological weak crystallization Hamiltonian and the structural correlators of the ideal macromolecules.

   3. The phenomenological and microscopic theories of the conventional (body-centered cubic, hexagonal and lamellar) and non-conventional (gyroid, bcc2, face-centered cubic, simple cubic etc.) phases in block copolymers.

   4. The SAXS data and other experimental methods to locate the phase diagrams of the weak crystallized polymer systems. Fluctuation (Brazovskii-Fredrickson-Helfand) effects and their experimental confirmation.

   5. Non-centrosymmetric lamellar phase in block copolymer blends: experiment.

   6. Phenomenological theory of non-centrosymmetric lamellar phase in the degenerate many-component weak crystallized systems.

1. G.E. Volovik
   CLASSICAL AND QUANTUM REGIMES OF THE SUPERFLUID TURBULENCE

   We discuss the turbulence of quantized vortex lines in connection with recent experiments in superfluid 3He [1]. This turbulence is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re = UR/ ν in classical hydrodynamics. It marks the transition between the "laminar" and "turbulent" regimes of vortex dynamics as suggested by recent experiments in Helsinki. The developed turbulence described by Kolmogorov cascade occurs when Re ›› 1 in classical hydrodynamics, and it must occur at q ‹‹ 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number Re_s = UR/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized forming fat vortex tubes, so that the quantization is not important; (ii) the quantum turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested [2].

   [1] A.P. Finne, T. Araki, R. Blaauwgeers, V.B. Eltsov, N.B. Kopnin, M. Krusius, L. Skrbek, M. Tsubota, and G.E. Volovik, "An intrinsic velocity-independent criterion for superfluid turbulence", Nature 424, 1022-1025 (2003).

   [2] G.E. Volovik, "Classical and quantum regimes of the superfluid turbulence", Pis'ma ZhETF 78, 1021-1025 (2003).

1. F. Bezrukov, D. Levkov, V.RUBAKOV (INR, Moscow) C. Rebbi (Boston U.), P. Tinyakov (EPFL, Lausanne and INR, Moscow)

   INSTANTON-LIKE BARYON NUMBER VIOLATION IN HIGH-ENERGY ELECTROWEAK COLLISIONS

   We make use of a semiclassical method for calculating the suppression exponent for topology changing transitions in high-energy collisions. In the Standard Model these processes are accompanied by violation of baryon and lepton number. By using a suitable computational technique we obtain results for s-wave scattering in a large region of initial data. Our results show that baryon and lepton number violation remains exponentially suppressed up to very high energies of at least 30 sphaleron masses (250 TeV). We also conclude that the known analytic approaches inferred from low energy expansion provide reasonably good approximations up to the sphaleron energy (8 TeV) only.

1. J. Zaanen, Z. Nussinov, and S. I. Mukhin

   DUALITY IN 2+1 D QUANTUM ELASTICITY: SUPERCONDUCTIVITY AND QUANTUM NEMATIC ORDER

   Superfluidity and superconductivity are traditionally understood in terms of an adiabatic continuation from the Bose-gas limit. We do not use this approach. Taking the theory of quantum elasticity (describing phonons) in a 2+1 D Bose system as a literal quantum field theory, we show that superfluidity and superconductivity (in the EM charged case) emerge automatically when the shear rigidity of the elastic state is destroyed by the proliferation of topological defects (quantum dislocations). We consider the nematic states, corresponding with condensates of dislocations, with Burgers vectors as topological charges, under condition that disclinations remain massive. Due to glide principle for dislocations in 2+1 D the compression rigidity decouples from the dislocation condensate and stays massless. The shear rigidity does not decouple, and as a result the shear modes acquire a Higgs mass in the dual (dislocation) condensate. Hence, the fluids are characterized by an isolated massless compression mode and are therefore superfluids (Landau criterium reconfirmed!). We also consider different ordered/disordered states of Burgers vectors calling them "Coulomb nematic" and "quantum smectic" of a novel kind. Finally, we find that the Higgs mass of the shear gauge fields, becoming finite in the nematic quantum fluids, automatically causes a Higgs mass in the electromagnetic sector by a novel mechanism. Hence, a new hydrodynamical way of understanding the conventional electromagnetic Meissner state (superconducting state) is proposed.

1. V.F.Gantmakher (Institute of Solid State Physics)

   SPECIFIC FEATURES OF THE INSULATOR FORMED UNDER THE SUPERCONDUCTOR-INSULATOR TRANSITION

   Various experimental observations of the magnetic-field-induced superconductor-insulator transition are described and compared with different theoretical models: one based on boson-vortex duality (Girvin, M.P.A. Fisher, et al.), next exploring the properties of granular superconductors (Beloborodov and Efetov) and the third analyzing effect of the superconducting fluctuations in the magnetic field at low temperature (Galitski and Larkin). All the models point to the existence of pairwise electron correlations at the Fermi-level of the insulator (so-called localized pairs) which should vanish in high magnetic fields. The localized pairs apparently come from the parity effect in ultra small quasigrains - local minima of the random potential which can admit only small limited number of electrons.

1. A.A.Belavin

   A SHORT INTRODUCTION TO CONFORMAL FIELD THEORY AND ITS INTEGRABLE PERTURBATIONS, Part II

1. Yurii E. Lozovik (Institute of Spectroscopy, Troitsk)

   SUPERFLUID AND CRYSTAL PHASES IN BILAYER SYSTEM

   Bilayer electron-hole and electron-electron systems are considered. Phase diagram, transport, drag effect, optical properties and Josephson phenomena will be reviewed. Liquid excitonic phase will be analyzed. Light backscattering in excitonic condensate will be reported. The electron-hole system in strong magnetic field will be considered.
   Pairing in composite fermion bilayer is analyzed. The problem of BCS instability of compressible unpaired quantum Hall bilayer state at nu = 2 x 1/(2m) total filling fraction in large interlayer separation, d, limit is discussed. Microscopic analysis is carried out within the framework of composite fermion formalism. Gauge field fluctuations both diagonal and off-diagonal on layer indexes is taken into account. The first defines singular renormalization in one layer and leads to marginality of composite fermion liquid; the nondiagonal contribution defines interlayer interaction. Interlayer composite fermion attraction governed by antisymmetric density fluctuations is taken into account. The role of marginality on BCS pairing is analyzed. The quantum phase transition governed by interlayer separation is discussed.

1. Kees van der Beek (Ecole Polytechnique, France) in collaboration with S.Colson, M.Konczykowski, Y.Matsuda, M.Gaifullin, P.Gierlowski, I.Abalosheva, M.Li, P.Kes VORTEX PHASE DIAGRAM IN CLEAN AND DISORDERED LAYERED SUPERCONDUCTORS

   The (B,T) phase diagram in layered superconductors in a magnetic field can be characterized by two transitions of the vortex lattice: a first order phase transition, commonly called vortex lattice melting, from a ''vortex solid'' to a ''vortex liquid'' without long range phase coherence, and a ''depinning'' transition above which no critical current can be measured. The two transitions follow quite different B(T) dependences, and can be studied independently by tuning material parameters, strength of disorder, or magnetic field. In the layered superconductor Bi2Sr2CaCu2O8, vortex fluctuations leading to either transition can be studied using the Josephson Plasma Resonance. In the first part of the talk, I shall present measurements in the ''vortex solid'' phase, at fields close to the first order transition field. The results show the predominant role of the vortex line tension, and the near-irrelevance of the vortex lattice shear modulus. This result is underscored by the observation of the first order transition in Bi2Sr2CaCu2O8 containing strong columnar pins. Finally, I shall present results obtained at higher fields, near the ''depinning'' or ''delocalisation'' transition. The results are put into perspective by a conjecture about the nature of the two transitions in magnetic field.

2. Jean-Eric Wegrowe (Ecole Polytechnique, France) MAGNETIZATION REVERSAL AND TWO LEVEL FLUCTUATIONS BY SPIN-INJECTION IN A FERROMAGNETIC METALLIC LAYER

   Slow magnetic relaxation and two level fluctuations measurements under high current injection is performed in single-contacted ferromagnetic nanostructures. The magnetic configurations of the samples are described by two metastable states of the uniform magnetization. The current-dependent effective energy barrier due to spin-transfer from the current to the magnetic layer is measured. The comparison between the results obtained with Ni nanowires of 6 $\mu$m length and 60 nm diameter, and Co (10 nm) / Cu (10 nm) / Co (30 nm) nanometric pillars of about 40 nm in diameter refined the characterization of this effect. It is shown that all observed features cannot be reduced to the action of a current dependent effective field. Instead, all measurements can be described in terms of an effective temperature, which depends on the current amplitude and direction, and on the magnetization state. The effective temperature is measured to be about 2000 K for 1 mA in nano-pillar structures, and 30 000 K for 1mA in Ni nanowires (far beyond the Curie temperature). The system is then analogous to an unstable open system. The effect of current induced magnetization reversal is interpreted as the balance of spin injection between both interfaces of the ferromagnetic layer.

1. A.A. Belavin

   A short intorduction to conformal fiel theory (CFT) and its integrable pertrubations.
   

   Part I.

   Critical behaviour and conformal symmetry.
   Conformal symmetry in two dimensions.
   Operator products expansion. Conformal bootstrap.
   Classification of conformal field thories.
   Minimal models of CFT. Spectrum of dimensions.
   Correlation functions in CFT.
   

1. V.B. Timofeev. O bose-condensatsii mezh'yamnyh exitonov.
   No annotation presented.

1. V.E. Zakharov. Self-consistent solutions in the weak turbulence and experiment.
   No annotation presented.

1. M.I. Vysotsky (ITEP). CP-violation for B-mesons and status of neutrino oscillations.
   No annotation presented.

1. Petr Fedichev (Universitet Innsbruck, Austria). Modelling of exotic quantum systems on optical lattice
   No annotation presented.

1. E. Kats. Growth in systems of vesicles and membranes.
   A simple phenomenological model of nucleation and growth in systems of vesicles and membranes is presented and analyzed. It is shown that the process of vesicle growth can be understood as a certain "reaction" and the driving force for this reaction is determined by anharmonic contributions to the curvature elasticity. Assuming that the aggregation is controlled by diffusion a simple kinetic approach predicts that the average radius increases in time $t$ as $t^{1/6}$ in close agreement with experimental data.
2. A. Dyugaev. Surface tension of liquid helium.
   The temperature dependence $\sigma (T)$ of liquid $He^3$ and $He^4$ is determined in the intermediate temperature region when $He^3$ and $He^4$ are quantum but not degenerate liquids. This dependence is given by the universal law $\sigma (T) - \sigma (0) \propto T^2$ that is related to the contribution of the surface energy levels of helium vapor. These discrete levels also alter the mobility of electrons on the surface of liquid helium or of solid hydrogen. The work is joint with P. Grigoriev.

1. Yu. N. Ovchinnikov. Collapses for non-linear Schroedinger equation.
   No annotation presented.

1. V.L. Saveliev (Institute of Ionosphere). Collision group and renormalization of the Boltzmann collision integral.
   On the basis of a recently discovered collision group, the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

1. V. Lebedev. Elastic turbulence: experiment and theory We are going to discuss a new phenomenon recently discovered experimentally by Groisman and Steinberg. It is the so-called elastic turbulence which is a random flow developed in weak polymer solutions at small Reynolds numbers. The reason for the chaotic state is in elastic instabilities which are relevant when the characteristic time of the flow fluctuations is of the order of the polymer relaxation time. The most interesting experimental data concern mixing, since the elastic turbulence is in some sense the ideal mixer. A research experimental information is obtained concerning statistical properties of the passive scalar advected by the chaotic flow in the elastic turbulence regime. The statistics admits a detailed theoretical derivation. We give a comparison of the theory and the experimental data.

1. Y. Pugai. On infinite symmetries in integrable lattice models and the corner transfer matrix approach.
   During last ten years the algebraic approach based on vertex operators has been applied for finding exact integral representations for correlation functions and form-factors in many exactly solvable two-dimensional models of statistical mechanics. This approach can be treated as a natural generalization of the Baxter Corner Transfer Matrix method. Using off-critical RSOS models as an example I would like to briefly discuss some properties of corner transfer matrices and give their algebraic interpretation in the spirit of the conformal field theory Virasoro algebra approach. Finally I would like to report on some recent results for correlation functions of Z(N) symmetric models based on the deformed parafermionic algebra.

1. A.Degaperis, S.V.Manakov, P.Santini (Dipartamento di Fisica, Universita di Roma la Sapienza). Boundary value problems for integrable PDE's.
   We review recent developments in the study of the Dirichlet and Newmann boundary value problems for linear and soliton PDE's.

1. G.E. Volovik. Kelvin-Helmholtz instability in superfluids and balck hole horizon at the brane separating two quantum vacua.
   An analog of black hole can be realized in the future experiments in Helsinki. The horizon can be constructed for the `relativistic' ripplons (surface capillary-gravity waves) living on the `brane' represented by the interface between two superfluid vacua, 3He-A and 3He-B, sliding along each other without friction. Similar experimental arrangement has been already used in ROTA experiments for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids.
   The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold which has been measured in recent experiments corresponds to appearance of the ergoregion for ripplons (the region where ripplons have negative energy in the frame of the environment). In the shallow-water geometry this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region beyond the ergosurface or horizon, the brane quantum vacuum is unstable due to interaction of brane matter (ripplons) with bulk matter (quasiparticles living in the higher-dimensional world of bulk superfluids). The development of this instability results in nucleation of vortices in 3He-B and shrinking of the black hole horizon. This mechanism of the black hole decay can be faster than due to the traditional Hawking radiation.
   The second critical velocity, the proper Kelvin-Helmholtz instability threshold, corresponds to the `physical' singularity inside the black hole, where the determinant of the effective metric becomes infinite.

1. D. Podolsky. Cosmology near singularity.
   We discuss classical and quantum properties of several string-inspired cosmological models. The subject of main interest for us is their behaviour near the cosmological singularity where one should expect strong discrepancies between Einstein-Hilbert general relativity and gravitation described by string low-energy effective action.

1. B.G. Zakharov. Light-cone integral approach to the Landau-Pomeranchuk-Migdal effect in QED and QCD. In 1953 Landau and Pomeranchuk predicted within classical electrodynamics that multiple scattering can suppress considerably bremsstrahlung of high energy charged particles in medium. Later, in 1956 Migdal developed a quantum theory of this effect (usually called the Landau-Pomeranchuk-Migdal effect).
   In this talk I discuss a new approach to the LPM effect based on the path integral treatment of multiple scattering. The approach is also applicable to gluon emission from a fast quark in a hot QCD matter. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed in terms of the Green function of a two-dimensional Schrodinger equation with an maginary potential. In QED this potential is proportional to the dipole cross section for scattering of an e e- pair off an atom, while in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a color center.
   In the case of QED we compare theoretical predictions with the first accurate data on the LPM effect obtained at SLAC. For most of the targets our predictions are in excellent agreement with the experimental data.

1. V.I. Marchenko, E.R. Podolyak. Wetting transition in superconductivity.
   No annotation presented.

1. V.Ignatovich. Waves and particles in layered media.
   We deduce and demonstrate simple analytical formulas for calculation of scattering of waves and particles in multilayered systems. In particular, reflection and transmission in quantum mechanics for arbitrary periodic potentials with finite number of periods. Algorithm for preparation of supermirror, or filters. Calculation of bound levels splitting in periodic potentials. Diffraction in three dimensional periodic systems. New form of dynamical diffraction in single crystals.

1. N.M. Chtchelkatchev. Spin transport in superconducting hybrid structures.
   Not long ago emerged new direction in mesoscopic physics dealing with spin transport in nanostructures (traditionally mesoscopic physics deals with (coherent) electron transport in nanostructures). One of the important questions is description of spin transport in superconducting hybrid mesoscopic structures. For example, consider a beam of spin-polarized electrons scattering from thin superconducting region. It turns out that the superconductor at certain conditions plays the role of spin-filter separating the spin-current from the charge current. Consider now a beam of Cooper pairs (supercurrent) going through a constriction from one superconductor to another one. The constriction plays the role of quantum dot for Bogoliubov quasiparticles (Andreev quantum dot (AQD) is a superconducting junction where Bogolyubov quasiparticles can be trapped in discrete Andreev levels). Andreev levels in superconducting junctions are in general spin-degenerate. However in the presence of magnetic/exchange field or spin-orbit interaction spin degeneracy is lifted. Sometimes it is feasible to manipulate individual spin-state in an AQD. It can be shown that AQD can be brought into spin-1/2 state. The coupling between spin and superconducting current facilitate manipulation and measurement of this state in comparison with common semiconductor quantum dots. AQD's coupled inductively can serve as a solid-state base for universal quantum computing.

1. N.B. Kopnin, A.S. Mel'nikov, V.M. Vinokur. Single-electron transport through the vortex core levels in clean superconductors.
   We investigate the low temperature electron transport in N-S-N structures in the presence of vortex lines perpendicular to the interfaces. It is shown that, in the absence of elastic scattering at the interface, the single-electron transport along the vortices in clean superconductors is not determined by the density of states in vortex cores. Within the quasiclassical approach the vortex contribution to the transport is determined by resonance tunneling of electrons via vortex core levels. We calculate the thermal conductance in the direction along the magnetic field and show that it decays with an increase in the superconducting slab thickness.

1. S.L. Ginzburg and N.E. Savitskaya (Petersburg Nuclear Physics Institute). Self-organization of the critical state in granular superconductor.
   We study the critical state of a one-dimensional multijunction SQUID with a random arrangement of junctions in an increasing magnetic field. Using two mathematical models (system of differential equations for gauge-invariant phase differences and a simplified algorithm), we show that the system demonstrates a self- organized behavior. An intrinsic spatial randomness introduced into the model allows us to obtain self-organization in one-dimensional case under fully deterministic perturbation. We also show that our simplified algorithm represents a new model of a self-organized criticality.

1. P.I. Arseyev (Lebedev Physical Institute). Coulomb correlation effects in the tunelling spectroscopy of individual impurities.
   Some non-equilibrium Coulomb effects in resonant tunnelling through deep impurity states are analyzed. It is shown that corrections to the tunnelling vertex caused by the Coulomb interaction can result in nontrivial behavior of the tunnelling characteristics and should be taken into account. One encounters with effects similar to the Mahan edge singularities in the problem of X - ray absorption spectra in metals. One might expect in this situation a smeared power-law singularity in current-voltage characteristics near the threshold voltage.

1. V. Golo (MSU). The elasticity of single DNA molecules (a review).
   The mechanical properties of the DNA molecule have been a subject of intense study for the last few years. The current approach is to consider DNA as a worm-like chain. The model allows for explaining major experimental results, but still there are questions to the effect, especially concerning the elastic behaviour as a function of the ionic strength of the solvent. In particular it contradicts the familiar model of elastic rod often used for describing DNA.
2. V. A. Benderskii (ICP). Instanton approach to quantum chemical dynamics.
   Quantum chemical dynamics is based on the eigenvalue problem for multidimensional vibration Hamiltonians with potential energy surfaces (PES) having at least two minima, which are associated with the initial and final quasi-stationary states, reactants and products of chemical reaction. Although a semiclassical approximation is to be valid, commonly used WKB methods appear to be ineffective for multidimensional problems due to singularities of WKB solutions on caustics. Instanton approach (IA) differs from WKB method by replacement of energy as the quantity of h-order from Gamilton-Jacobi equation into transport equation. IA allows us to solve the Landau-Zener problem in the configuration space representation and derive the quantization rules for intersecting diabatic potentials at an arbitrary value of adiabatic coupling. In multidimensional IA, the minimum action path (MAP) is found from the classical equation of motion and then the Euclidean action is calculated in the vicinity of MAP as the expansion over the powers of transverse displacements with tunneling coordinate dependent coefficients. Coherent-incoherent transitions in the asymmetric double-well potentials and vibration stimulated tunneling are discussed as examples of IA applications.

1. G.A. Alekseev (Steklov Institute). Gravitational fields described by integrable reductions of Einstein's field equations.
   Einstein's equations for gravitational fields in vacuum, the Einstein - Maxwell and Einstein - Maxwell - Weyl equations for gravitational, electromagnetic and massless Weyl spinor fields, some string theory induced gravity models with electromagnetic, axion and dilaton fields are known to become integrable, if the space-time admits the Abelian two-dimensional isometry group and all field components and their potentials are dependent on some two of the four space-time coordinates only. In the talk we consider a number of specific features of very rich and universal (i.e. common for all these integrable cases) internal structure of reduced Einstein's equations which gave rise to a development of some general and simple approach to solution of these equations which can be called as the "monodromy transform" approach. This approach has provided a convenient base for further development of some effective methods for construction of solutions with wanted physical and geometrical interpretation, superposition of some known field configurations, generation of infinite hierarchies of solutions with infinitely increasing number of parameters and gave rise to the linear algorithms for solutions of the Cauchy and characteristic initial value problems for the reduced Einstein's equations. We also discuss particular examples of the solutions corresponding to physically different types of field configurations, such as the black holes immersed into the external gravitational and electromagnetic fields, various types of waves with smooth profiles or distinct wavefronts colliding on the Minkowski background or propagating in some other space-times, the waves emitted by accelerated sources, dynamics of some inhomogeneous cosmological models, and describe their physical and geometrical properties.

1. M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev. Shedding and interaction of solitons in weakly disordered optical fibers
   Propagation of a soliton pattern through an optical fiber with weakly disordered dispersion is considered. Solitons, perturbed by this disorder, radiate, and, as a consequence, decay. The average radiation profile and the degradation law of a single soliton is found. The emergence of a long-range intra-channel interaction between the solitons, mediated by the radiation, is reported. We show that soliton in a multi-soliton pattern experience a random jitter: average force acting on a soliton is negligible and fluctuations of the soliton velocity are Gaussian, with a typical fluctuation proportional to square of the distance passed by the soliton in the fiber and to square root of the information rate (number of solitons per unit length of the fiber). We also present results of direct numerical simulation of the soliton decay and two-soliton interaction, confirming our theoretical analysis.

1. K. Saraikin. N=1 supersymmetric gauge theories and geometry.
   We will review recent progress in gauge theories with minimal (N=1) supersymmetry: confinement, instanton corrections, superpotentials, relation with Seiberg-Witten theory etc. In particular, we will discuss how low-energy effective action of such theories can be reproduced in pure geometrical terms using certain (Calabi-Yau) three dimensional complex manifolds.

1. A.A. Starobinsky. Trans-planckian particle creation in cosmology.
   If the Lorentz invariance is broken (or "deformed") at some large energy close to the Planckian one, so that the dispersion law for elementary particles \omega(k) differs from the standard one, the expansion of the Universe may result in gravitational creation of pairs of particles and antiparticles with a very high energy. The expansion of the Universe (both at present time and in the early Universe) gradually redshifts momenta of all Fourier modes of a quantum field and transports them from the trans-Planckian region of very high momenta to the sub-Planckian region where the standard particle interpretation is valid. Then, if the WKB condition is violated somewhere in the trans-Planckian region, the field modes enter the sub-Planckian region in a non-vacuum state containing equal number of particles and antiparticles.
   This effect, if exists at all, can be found or limited by cosmological observations. The most restrictive upper limit follows from the number of ultra-high energy cosmic rays created now. In turn, their total amount can be shown to be bounded by the cosmic diffuse gamma-ray background. This limit rules out the possibility to detect signatures of such short distance effects by studying the temperature anisotropy of the cosmic microwave background. On the other hand, a remarkable possibility that some part of observed ultra-high energy cosmic rays originates from new trans-Planckian physics remains open.

1. Giancarlo Jug. Statistical mechanics of magnetic-field sensitive structural glass.
   Recent experiments on the thermal, dielectric and acoustic properties of multicomponent glasses at low temperatures have revealed an unusual response in some window-glasses to a weak applied magnetic field. A statistical-mechanics theory will be presented to explain quantitatively, at least in part, these puzzling experimental findings. The theory is based on an extension of the standard tunneling model for structural low-temperature glasses and on the mean-field theory of spin-glasses, suitably adapted to the problem.

1. V.E. Zakharov. Dynamics of Bose condensation.
   No annotation presented.

1. V.V. Lebedev. Acceleration of chemical reactions by chaotic mixing.
   A comprehensive theory of the binary chemical reaction A+B->C in chaotic flows at large Schmidt (Sc) and Damk\"{o}hler (Da) numbers, and with initially injected equal (or close to equal) amounts of both chemicals, is developed. The combined effects of advection and diffusion are important and result in essential enhancement (in comparison with a situation without advection) of the overall reaction rate. Diffusion controls the fluxes of chemicals towards the interface separating the chemicals, while advection increases area of the interface. We identify four different stages of the spatio-temporal evolution. The chemicals are well separated during all but the final (and the only spatially uniform) stage. The relatively complex division of the evolution into the stages is due to finite-size effects which appear when the chemical reaction rate is controlled by the bulk, peripheral, and boundary domains of the flow.

1. L. Levitov. Internal waves and synchronized precession in a cold vapor.
   It was shown by E. Bashkin in 1981 that exchange in a Boltzmann gas of bosons with several internal states leads to collective transport of internal polarization. The internal dynamics can be understood as Larmor precession in the presence of a torque induced by atoms on each other via exchange coupling. In a recent experiment carried out in JILA, collective waves of internal state polarization in a cold magnetically trapped Rb vapor were observed by a new spatially resolved technique. A generalized Bloch equation that includes interatomic exchange effects as well as orbital motion in the gas is derived and used to interpret the JILA experiment. It is predicted that exchange leads to formation of domains in which precession frequencies are synchronized.
   (M. Oktel and L.L., PRL 88, 230403, 2002)
2. R. Arhipov. On the motion of muplicharge bubbles in helium. (short communication)
   No anntotation.

1. A.A. Belavin. On integrable systems connected with quantum groups in root of unity.
   Centre of Quantum Group (QG) in root of unity is extended. It makes possible to perform Quantum Group reduction of Integrable model connected with the QG. It can be shown that after this Quantum Group reduction the transfer-matrices of the model satisfy the closed system of the truncated functional relations.
2. A. Odesskii. Quantization of some cubic Poisson brackets.
   We discuss the problem of quantization of certain class of Poisson structures, for example {x,y}=z^3, {y,z}=x^3, {z,x}=y^3. Our main tool is invariant pseudodifferential operators on the complex half-plane.

1. E.S. Pikina and V.E. Podnek. Simple interfacial model of surface-induced smectic layering in liquid crystals.
   We propose simple interfacial model of surface-induced smectic layering (quantized wetting layer growth) observed just above the bulk isotropic-smectic A phase transition in liquid crystals [1]. The model generalizes known interfacial models of critical wetting and roughening transition. It is shown that smectic wetting in the layering regime is always incomplete. The comparison with experimental data is made.
   [1] B.M.Ocko, A.Braslau, P.S.Pershan, J.Als-Nielsen, and M.Deutsch, Phys.Rev.Lett., 1986, vol. 57, p. 94

1. L.B. Ioffe and M.V. Feigelman. Possible realization of an ideal quantum computer in Josephson junction array with topologically protected degenerate ground states.
   We introduce a new class of Josephson arrays which have non-trivial topology and exhibit a novel state at low temperatures. This state is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. These arrays have degenerate ground states with this degeneracy 'protected' from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction and show that even a small array exhibits interesting physical properties such as superconductivity with double charge, 4e, and extremely long decoherence times.

1. S.V. Iordanski, A. Kashuba. The ground state and excitations in 2deg in magnetic field at large Coulomb interaction.
   Some general properties of possible classification of the ferromagnetic ground state are investigated. The spectrum of the low energy collective excitations consists of Kohn exciton and gapless spin exciton. It is shown that the energy of topological excitations (skyrmions) is lower than the cyclotron energy (at large Coulomb interaction) and does not contain the large exchange energy typical for opposite case of extremely large magnetic field.

1. E.A. Kuznetsov. Collapse in hydrodynamics and Kolmogorov spectrum.
   No annotation presented.

1. A.V. Toporensky (Sternberg Astronomical Institute). Isotropisation of Bianchi I brane cosmological models.
   The problem of isotropisation of Bianchi I brane cosmological model is described. It is shown that unlike a standard scenario the presence of an ordinary matter with a positive pressure enlarges anisotropy of a brane at early stages of cosmological expansion (when brane corrections to Einstein equations are significant). A possible influence of an anisotropic stress on the brane dynamics is also discussed.

1. A. V. Syromyatnikov (St. Petersburg). Hidden long range order in Heisenberg Kagome antiferromagnets.
   We give a physical picture of the low-energy sector of the spin 1/2 Heisenberg Kagome antiferromagnet (KAF). It is shown that Kagome lattice can be presented as a set of stars which are arranged in a triangular lattice and contain 12 spins. Each of these stars has two degenerate singlet ground states which can be considered in terms of pseudospin. As a result of interaction between stars we get Hamiltonian of the Ising ferromagnet in magnetic field. So in contrast to the common view there is a long range order in KAF consisting of definite singlet states of the stars.
2. V. N. Rodionov, G. A. Kravtsova, and A. M. Mandel (Moscow). The threshold processes in external electromagnetic fields.
   The threshold processes in external electromagnetic fields of some configurations are considered. The decay of quasistationary states is studied by means of the probability equations. Starting with these equations, we obtain the expressions for complex energy as a function of the field. Moreover, asymptotics for Re and Im parts of the energy are studied. In particular, we prove the absence of the stable action of magnetic field for some configurations and discuss consequences of this result.

1. M. Lashkevich. Bosonisation techniques in the theory of exactly solvable models.
   It is a review of bosonization techniques, their advantages and problems. These techniques take their origin in Baxter's corner transfer matrix approach and bosonization of conformal field theory. Bosonization makes it possible to calculate exactly short-range correlation functions and form factors in a class of lattice models. In the case of models of quantum field theory similar techniques are related to quantization in the Rindler coordinates and provide exact integral expressions for form factors.

1. A.M. Dyugaev. Nuclear ferromagnetism induced Fulde-Ferrel-Larkin-Ovchinnikov state. We present a theoretical study of the influence of the nuclear ferromagnetism on superconductivity in the presence of the electron-nuclear spin interaction. It is demonstrated that in some metals, e.g. Rh, W, the BCS condensate imbedded in a matrix of ferromagnetically ordered nuclear spins should manifest the FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) state. We outline that the optimal experimental conditions for observation of FFLO could be achieved by creation, via adiabatic nuclear demagnetization, of the negative nuclear spin temperatures. In this case the nuclear polarization points in the opposite to the external magnetic field direction and the electromagnetic part of the nuclear spin magnetization compensates the external magnetic field, while the exchange part creates the nonhomogeneous superconducting order parameter.

1. A.G. Lebed. Charge-density wave (CDW) and spin-density-wave (SDW) phases induced by a magnetic field in low-dimensional solids.
   A cascade of the metal-CDW phase transitions (recently discovered by D.Anders et al.) and the cascades of the metal-SDW transitions (which are observed in some low-dimensional organic conductors) are theoretically analyzed. We calculate the transition temperatures and free energies of the CDW and SDW subphases induced by a magnetic field. For CDW, we predict novel kind of an angular resonance and a novel type of a metal-DW phase diagram. We discuss the connections of our results with the existing experimental data including the so-called "three-dimensional quantum Hall effect".

1. Yu. N. Ovchinnikov. Critical fields in supreconductors.
   No annotation presented.

1. S.V. Demishev (General Physics Institute of RAS). Effects of doping and disorder on the spin-Peierls state (experiment).
   1. Introduction. Organic and inorganic spin-Peierls materials. Universal properties of spin-Peierls materials: magnetic phase diagram and concentrational phase diagram. Specific case of CuGeO3.
   2. Universality vs. experiment (cases of CuGeO3 and MEM(TCNQ)2). Discussion of the Mostovoi and Khomskii calculation of the concentrational phase diagram.
   3. Outside the universal scenario: the case of CuGeO3 doped with magnetic impurities.
   4. Specific problems of ESR in the 1D s=1/2 antifferomagnetic chains. Latest developments.

1. Yu. S. Barash, A. M. Bobkov and M. Fogelstrom. Josephson current between chiral superconductors. We study chiral interface Andreev bound states and their influence on the Josephson current between clean superconductors. Possible examples are superconducting Sr$_2$RuO$_4$ and the $B$-phase of the heavy-fermion superconductor UPt$_3$. We show that, under certain conditions, the low-energy chiral surface states enhance the critical current of symmetric tunnel junctions at low temperatures. The enhancement is substantially more pronounced in quantum point contacts. In classical junctions dispersive chiral states result in a logarithmic dependence of the critical current. This logarithmic behavior contains the temperature, the barrier transparency and the broadening of the bound states, and depends on the detailed relation between these parameters. The Josephson current through the domain wall doesn't acquire this logarithmic enhancement, although the contribution from the bound states is important in this case as well.

1. Victor Berezin (Institute for Nuclear Research RAS). Towards the theory of quantum black holes.
   Everybody knows what the classical black holes are.
   The main feature that characterizes black holes and distinguishes them from other physical objects is their universality. Such an universality is widely known as the "no hair conjecture". It means that everything that can be radiated away does radiate during the gravitational collapse, and the resulting black hole is described by only few parameters, namely, by its mass, angular momentum and gauge charges. The universal character of black holes allowed J.Bekenstein to put forward an analogy between black hole physics and thermodynamics. According to Bekenstein, the black hole is endowed by some temperature and entropy, the value of entropy being proportional to the area of the event horizon. The rigorous proof of four laws of thermodynamics for the most general stationary black holes was given by Bardeen, Carter and Hawking. And at the top of these is Hawking's discovery that a black hole does radiate as a black body with this very temperature. S. Hawking considered a quantized scalar field on the given Schwarzschild background and showed that it is nontrivial causal structure of the black hole metric that is responsible for the black body radiation. Such an effect is purely quantum, and the Hawking temperature is a generalization of the Unruh temperature seen by an uniformly accelerated observer in the flat spacetime. The analogy between these two effects illustrates the famous equivalence principle.
   The discovery of the black hole evaporation opened, in a sense, the quantum era in the black hole physics. The matter is that the very definition of the black hole involves the notion of the so called event horizon (which is the boundary between geodesics that can escape to infinity and those that cannot). The event horizon can be determined only globally, and the procedure requires knowledge of the whole history. Since, due to evaporation, the black holes disappear (at least, if do not take into account the back reaction of the radiation on the spacetime metric) the very notion of the black hole becomes only approximate.
   Why should we study quantum black holes? First, this problem is interesting by itself and it could provide additional links between General Relativity and Quantum Theory. Second, at the final stage of evaporation black holes are so small that quantum effects can no more be ignored. Third, small black holes can be formed by large enough fluctuations of both matter fields or spacetime metric in the Very Early Universe (the so called Primordial Black Holes) or in the course of vacuum phase transitions. But how small should be a black hole in order to be considered as a quantum object? On purely dimensional grounds using Newton's constant $G$, Planck's constant $\hbar$ and velocity of light $c$, we are able to construct two different quantities with the dimension of length for some object of mass $m$, namely, the Compton length $\lambdabar/mc$ and the gravitational (Schwarzschild) radius $r_g = 2 G m/c^2$. For masses much smaller than the Planckian mass $m_{Pl} = \sqrt{\hbar c/G}$ the gravitational radius is much smaller than the Compton length and the object is purely quantum (this also indicates that there may be no black holes with so small masses). If the mass is much higher than the Planckian mass, the Compton length is well inside the black hole horizon and in this case we are already have purely classical black holes (if it is possible, of course, to ignore the Hawking radiation). Thus, the range of quantum black hole masses is somewhere in-between. The first attempt to obtain the quantum black hole mass spectrum was due to J. Bekenstein. He noticed that an event horizon area for slowly evolving black holes is an adiabatic invariant. So, the usual quasiclassical quantization leads to an equidistant spectrum for a black hole surface area. In the case of the Schwarzschild black hole this results in the now famous square-root mass spectrum $m_{BH}\sim\sqrt{n}$, where $n$ is an integer quantum number. The same type of spectrum was then advocated by J.Bekenstein and S.Mukhanov later on by many others. It was shown also that such a spectrum is compatible with the Hawking radiation.
   In what follows we confine ourselves with consideration of the Schwarzschild (neutral, nonrotating) black holes only. The very fact that the mass (total energy) of black holes depends on only one quantum number $n$ can be viewed as a generalization of the "no hair" conjecture and confirms the universal character of black holes also on the quantum level. But we should pay some price for such a universality. And this price is that the every energy level is highly degenerate. Indeed, since the black hole entropy is proportional to the area of the horizon, and the latter has (approximately) an equidistant spectrum, the number of quantum states with the same total energy (mass) grows exponentially with the quantum number $n$. The real physical explanation of this phenomenon is still an open problem. In our opinion, this is because we do not yet know what is an object that could be called a quantum black hole. In other words, we need a definition. It seems it is the universality that could become the crucial feature which would distinguish quantum black holes from any other quantum object. It is worth noting that in the recent paper by G.Gour the equidistant spectrum for the black hole area and the exponential degeneracy of the energy levels have been taken as postulates. The author constructed the Hamiltonian operator and the algebra of observables for quantum Schwarzschild black holes and, thus, showed the selfconsistency of these two postulates. The abovementioned attempts to construct a theory of quantum black holes can be called phenomenological.
   The equidistant (or any other) black hole area spectrum which leads to a discrete mass spectrum poses one serious problem. The classical, in our case - Schwarzschild, black hole state is described by only one parameter, its mass, irrespective of how this black hole has been formed. Let us suppose that the black hole is formed by the collapse of gravitating particles. The motion of these particles can be either bound or unbound, such qualitative difference in the history of the constituents in no way reflected in the mass of the resulting black hole. This is not surprising in classical theory. But in quantum theory it does makes a difference. The bound motions give rise to discrete mass spectra while the mass spectra for unbound motions are continuous. And if the black hole mass spectrum is just the mass (energy) spectrum of this system of particles (what is the case in classical theory) we can easily distinguish the black holes formed due to bound motion from that formed due to unbound motion. But this contradicts the principle of universality (quantum "no-hair" conjecture). Then, what is it that gives the discrete mass spectrum for quantum black holes? Clearly, we need a deeper insight into the nature of these objects.

1. M.Yu. Kagan, K.I. Kugel, D.I. Khomskii. Inhomogenious charged states and phase stratification for manganites.
   Analiziruyutsya mekhanizmy elektronnogo fazovogo rassloeniya v oksidnykh materialakh tipa manganitov. Rassmotrenie provoditsya v ramkakh prostoy modeli kondo-reshetki s mezhuzel'nym kulonovskim ottalkivaniem elektronov. Eta model' pozvolyaet vyyavit' neustoychivost' odnorodnogo magnitnogo ili zaryadovogo uporyadocheniya otnositel'no obrazovaniya kapel'nykh struktur (magnitnykh polyaronov) v shirokoy oblasti parametrov fazovoy diagrammy. Issleduyutsya razlichnye tipy i formy magnitnykh polyaronov. Obsuzhdayutsya transportnye kharakteristiki i spektr shumov v fazovo-rassloennom sostoyanii.

1. E.V. Kholopov (Institute of Inorganic Chemistry). Uniqueness of electrostatic solutions in the bulk of perfect crystals.
   Although the investigation of lattice sums is a classical subject for more than a century, some problems concerned with their uniqueness in dependence on the mode of summation, as well as with the rate of convergence exist heretofore. In the present work a rigorous electrostatic theorem has been proved about the definite convergence of Coulomb sums over translation invariant lattices. As a result, any uniform potential contribution to bulk potentials is absent in perfect crystals. The topological nature of this issue is associated with the periodic boundary conditions invariant to the definition of the unit cell. The close relation between absolute local potentials and the bulk Coulomb energy is substantiated. It is principal that the analysis may be performed in terms of absolutely convergent series by means of the incorporation of fictitious charges appropriate to the case. As a result, the general criterion on admissible orders of the lattice summation is proposed. The shell-by-shell order of summation accounting for crystal fields is verified as universal. The numerical efficiency of the direct summation modified properly is exhibited in a set of various model cases, with including depolar sums. The topological nature of the Lorentz field becomes evident therefrom.

1. L.B. Ioffe, M.V. Feigelman, A.S. Ioselevich, D.A. Ivanov, M. Troyer, G. Blatter. Topologically protected quantum bits from Josephson junction arrays.
   All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev, holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer-liquid groundstate can be used in the construction of topologically stable qubits. We propose two implementations based on Josephson junction arrays and show how to construct the gates shifting the amplitude and phase of individual qubits and enforcing the entanglement of two qubits.

1. A.M. Gurin. Geometric attractor of an electron beam which has passed through a crystal.
   The Lemmlein algorithm assigns a cyclic interaction of a mathematical point with other (n+1) points of the n-dimensional Euclidean space. In this paper generalization A of the Lemmlein algorithm for an arbitrary number of points m situated in the n-dimensional Riemann space is proposed. Algorithm A generates a Markovian chain consisting of the finite number of combinatorially different strongly convergent attractors.

1. V.E. Zakharov. Weak turbulence. Present state of theory.
   No annotation presented.

1. A.Barvinsky (Lebedev Physical Institute). Brane-world effective action and origin of inflation.
   We construct braneworld effective action in two brane Randall-Sundrum model and show that the radion mode plays the role of a scalar field localizing essentially nonlocal part of this action. Non-minimal curvature coupling of this field reflects the violation of AdS/CFT-correspondence for finite values of brane separation. Under small detuning of the brane tension from the Randall-Sundrum flat brane value, the radion mode can play the role of inflaton. Inflationary dynamics corresponds to branes moving apart in the field of repelling interbrane inflaton-radion potential and implies the existence acceleration stage caused by remnant cosmological constant at late (large brane separation) stages of evolution. We discuss the possibility of fixing initial conditions in this model within the concept of braneworld creation from the tunneling or no-boundary cosmological state, which formally replaces the conventional moduli stabilization mechanism.