CONTENTS -- Foreword -- A MATRIX MODEL REPRESENTATION OF THE INTEGRABLE XXZ HEISENBERG CHAIN ON RANDOM SURFACES J. Ambjørn and A. Sedrakyan -- 1. Introduction -- 2. The model -- 3. The matrix model -- 3.1. The space of integration -- 4. Conclusions -- References -- MAGNETIZATION AND CONCURRENCE PROPERTIES OF DIAMOND CHAIN: TWO APPROACHES N. S. Ananikian, H. A. Lazaryan, M. A. Nalbandyan, O. Rozas and S. M. de Souza -- 1. Introduction -- 2. Gibbs-Bogoliubov approach -- 3. Magnetisation, specific heat and susceptibility -- 4. Concurrence and thermal entanglement -- 5. Ising-XXZ diamond chain and entanglement -- 6. Conclusions -- References -- COMPLETE (O7,O8) CONTRIBUTION TO B XS AT O(a2S)5 THEORY OF QHE H. M. Asatrian, T. Ewerth, A. Ferroglia, C. Greub and G. Ossola -- 1. Introduction -- 2. Results for the (integrated) photon energy spectrum -- 3. Estimating the numerical impact on Br( Xs ) -- 4. Summary and conclusions -- References -- NON-TRIVIAL HOLONOMY AND CALORONS P. van Baal -- 1. Introduction -- 2. The setting -- 3. Some properties of caloron solutions -- 3.1. Fermion zero-modes -- 3.2. Calorons of higher charge -- 4. More recent results -- Acknowledgments -- References -- SU(N) AND O(N) OFF-SHELL NESTED BETHE ANSATZ AND FORM FACTORS H. Babujian, A. Foerster and M. Karowski -- 1. Introduction -- 2. The "bootstrap program" -- Integrability -- The S-matrix -- 3. Form factors -- 3.1. Two-particle form factors -- 3.2. The general form factor formula -- 4. Examples -- 4.1. The chiral SU(N)-Gross-Neveu model -- 4.2. The nonlinear O(N) σ-model -- Acknowledgments -- References -- SPONTANEOUS BREAKING OF LORENTZINVARIANCE AND GRAVITONS AS GOLDSTONE PARTICLES Z. Berezhiani and O. V. Kancheli -- 1. Introduction -- 2. Tensor condensates and spontaneous Lorentz-violation -- 3. Tensor condensate oscillations and Goldstone gravitons.

3.1. Degenerate case -- 4. Einstein equations -- 5. Lorentz-violation in observables -- 6. The Goldstone graviton couplings: universality problem -- References -- ON EMERGENT GAUGE AND GRAVITY THEORIES J. L. Chkareuli -- 1. Introduction -- 2. Emergent gauge symmetries -- 3. Deriving diffeomorphism invariance -- 4. Graviton as a Goldstone boson -- 5. Summary and outlook -- Acknowledgments -- References -- GEODESIC MOTION IN GENERAL RELATIVITY: LARES IN EARTH'S GRAVITY I. Ciufolini, V. G. Gurzadyan, R. Penrose and A. Paolozzi -- 1. The problem of a material body in General Relativity -- 2. Space Experiment LARES -- References -- QUANTUM DOTS AND QUANTUM RINGS: REAL LOW DIMENSIONAL SYSTEMS I. Filikhin, S. G. Matinyan and B. Vlahovic -- 1. Introduction -- 2. Schrodinger equation and effective mass approximation -- 3. The non-parabolicity of the conduction band. The Kane formula -- 4. Effective approach for strained InAs/GaAs quantum structures: effective potential -- 5. Electron energy in quantum rings with varieties of geometry: effect of non-parabolicity -- 6. The C-V measurements and the effective model: choosing the parameters -- 7. Experimental data for InAs/GaAs QR and the effective model -- 8. Quantum Chaos in Single Quantum Dots -- 8.1. Quantum Chaos -- 8.2. The nearest neighbor spacing statistics -- 8.3. Violation of symmetry of the QD shape and nearest neighbor spacing statistics -- 9. Double Quantum Dots and Rings: new features -- 9.1. Disappearance of Quantum Chaos in Coupled Chaotic Quantum Dots -- 9.2. Electron transfer between rings of Double Concentric Quantum Ring in magnetic field -- References -- COLLECTIVE STATES OF D(D3) NON-ABELIAN ANYONS P. E. Finch and H. Frahm -- 1. Introduction -- 2. Integrable many anyon models -- 3. Bethe ansatz -- 4. Low energy spectrum of H -- 5. Low energy excitations of H0 -- 6. Phase diagram -- 7. Summary.

Acknowledgments -- References -- EFFECTIVE HAMILTONIAN FOR THE HALF-FILLED SPIN-ASYMMETRIC IONIC HUBBARD CHAIN WITH STRONG ON-SITE REPULSION I. Grusha and G. I. Japaridze -- 1. Introduction -- 2. The strong-coupling expansion approach -- 3. The Hubbard operators -- 4. Effective Hamiltonian in the half-filled band case -- 5. Conclusion -- Acknowledgments -- References -- HYPERBOLICITY VS RANDOMNESS IN COSMOLOGICAL PROBLEMS V. G. Gurzadyan and A. A. Kocharyan -- 1. Introduction -- 2. Instability of null geodesics in perturbed Friedmann-Robertson-Walker Universe -- 3. The degree of randomness of cosmic microwave background datasets -- Acknowledgments -- References -- ELECTROMAGNETIC PROPERTIES OF NEUTRINOS AT AN INTERFACE A. N. Ioannisian, D. A. Ioannisian and N. A. Kazarian -- References -- CORRELATIONS IN COSMOLOGICAL AND NONCOSMOLOGICAL SIGNALS H. G. Khachatryan, G. Nurbaeva, D. Pfenniger, G. Meylan and S. Sargsyan -- 1. Introduction -- 2. Correlations in cosmic microwave background maps -- 3. CMB and K-map power spectra -- 4. Cross correlations in cosmic microwave background temperature and K-maps -- 5. Conclusions -- Acknowledgments -- References -- BIG BOUNCE AND INFLATION FROM GRAVITATIONAL FOUR-FERMION INTERACTION I. B. Khriplovich -- Acknowledgments -- References -- CAPTURE AND EJECTION OF DARK MATTER BY THE SOLAR SYSTEM I. B. Khriplovich -- 1. Introduction -- 2. Total mass of dark matter captured by the Earth -- 3. Capture cross-section -- 4. Space distribution of captured dark matter -- 5. Back to the capture process -- Acknowledgments -- References -- TOPOLOGICAL THEORY OF QHE M. Kohmoto -- 1. Introduction -- 2. Hofstadter Butter.y -- 3. Bloch Electrons in a Uniform Magnetic Field -- 4. Linear Response Formula for the Hall Conductance -- 5. Chern Number, Hall Conductance, and Fiber Bundle -- References.

QCD STRING AS AN EFFECTIVE STRING Y. Makeenko -- 1. Introduction -- 2. QCD string as such -- 3. What to expect: QCD2 string -- 4. Effective string theory -- 5. Mean-field approximation for bosonic string -- 6. Comparison with Monte-Carlo data -- 7. QCD string as rigid string -- 8. Induced extrinsic curvature -- 9. Conclusion -- Acknowledgement -- References -- THE MUG: ON E = MC2 AND RELATIVITY THEORY IN THE MASS CULTURE L. B. Okun -- 1. Introduction -- 2. The text on the mug -- 3. My clarifications and comments -- 4. Four dimensions of the world -- NEW CHERN-SIMONS DENSITIES IN BOTH ODD AND EVEN DIMENSIONS E. Radu and T. Tchrakian -- 1. Introduction -- 2. Dimensional reduction of gauge fields -- 2.1. Descent over SN: N odd -- 2.2. Descent over SN: N even -- 3. New Chern-Simons terms -- 3.1. New Chern-Simons terms in all dimensions -- 3.2. Examples -- Acknowledgment -- References -- SPHERICAL SHELL COSMOLOGICAL MODEL AND UNIFORMITY OF COSMIC MICROWAVE BACKGROUND RADIATION B. Vlahovic -- 1. Introduction -- 2. Spherical shell model -- 3. Important implication of the model, uniformity of CMB -- 4. Justification for the spherical shell model -- 5. Conclusion -- Acknowledgments -- References -- PHOTON "MASS" AND ATOMIC LEVELS IN A SUPERSTRONG MAGNETIC FIELD M. I. Vysotsky -- 1. Introduction -- 2. D = 2 QED -- 3. Electric potential of the point-like charge in D = 4 in superstrong B -- 4. Hydrogen atom in the magnetic field -- 5. Screening versus critical nucleus charge -- Acknowledgments -- References -- CONSTRAINTS ON PARAMETERS OF THE BLACK HOLE AT THE GALACTIC CENTER A. F. Zakharov, F. De Paolis, G. Ingrosso and A. A. Nucita -- 1. Introduction -- 2. Shadows for Kerr black holes -- 3. Shadows for Reissner-Nordstrom black holes -- 3.1. Basic definitions and equations -- 3.2. Shadows for a Reissner-Nordstrom black holes with a tidal charge.

4. Conclusions -- Acknowledgments -- References -- DIFFUSION IN TWO-DIMENSIONAL DISORDERED SYSTEMS WITH PARTICLE-HOLE SYMMETRY K. Ziegler -- 1. Introduction -- 2. Model -- 2.1. Quantum diffusion -- 2.2. Hamiltonian -- 3. Functional-integral representation -- 4. Discussion -- Acknowledgment -- References -- AUTHOR INDEX.