Mathematical results in quantum physics : proceedings of the QMath11 Conference, Hradec Králové, Czech Republic, 6-10 September 2010

The volume collects papers from talks given at QMath11 -- Mathematical Results in Quantum Physics, which was held in Hradec Kr??lov?©, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Kralove was no exception. CONTENTS......Page 10 PREFACE......Page 6 CONFERENCE COMMITTEES......Page 8 PART A Plenary Talks......Page 13 1. Introduction......Page 15 2. Mathematical preliminaries......Page 17 3. Definitions of min- and max-relative entropies......Page 18 4. Properties of min- and max-relative entropies......Page 20 5. Min- and max-relative entropies and state discrimination......Page 24 6. The min- and max-relative entropies of entanglement......Page 25 7. Smoothed min- and max-relative entropies of entanglement and their operational interpretations......Page 28 References......Page 30 1. Definition and previous rigorous results......Page 33 2. The multi-polaron problem and new results......Page 35 2.1. Binding of multi-polaron systems......Page 36 2.2. Thermodynamic stability of multi-polaron systems......Page 37 3. Absence of bipolaron binding......Page 38 4. Polarons in one dimension......Page 39 References......Page 43 1. Introduction......Page 45 2. Short range interactions......Page 47 3. Coulomb interactions......Page 50 4. Peierls-Kekulé instability......Page 52 Acknowledgements......Page 54 References......Page 55 RENORMALIZATION OF DIRAC’S POLARIZED VACUUM......Page 57 1. A nonlinear Dirac equation......Page 58 The free vacuum......Page 59 Electrons interacting with the polarized vacuum......Page 60 2. Derivation from Quantum Electrodynamics......Page 61 3. Existence and non existence of solutions......Page 62 Existence of solutions......Page 63 Maximum ionization......Page 65 4. Renormalization......Page 66 Nonperturbative charge renormalization formula......Page 67 Asymptotic renormalization......Page 68 References......Page 70 2. Thick graphs......Page 72 2.1. Definition of a thick graph......Page 73 2.2. Examples of thick graphs......Page 76 2.3. Appearance of thick graphs in Physics and Mathematics......Page 78 3.1. Convergence results for Neumann Laplacians......Page 80 3.2. Convergence of operators in different Hilbert spaces......Page 82 4.1. Dirichlet Laplacians on thick graphs......Page 83 4.2. Difference between Neumann and Dirichlet case......Page 85 4.3. Other vertex conditions in the limit......Page 86 Acknowledgements......Page 88 References......Page 89 1. Introduction......Page 91 2. Density of States and the Semicircle Law......Page 93 3. Delocalization of Eigenvectors of Wigner Matrices......Page 98 4. Bulk Universality for Hermitian Wigner Matrices......Page 99 5. Extensions and Applications of Universality......Page 104 References......Page 105 1. Introduction......Page 107 2.1. Collections of Quantum Systems......Page 108 2.2. Interactions and Models......Page 109 2.3. Observables and Support......Page 110 2.4. From Locality to Commutators......Page 111 3.1. On the Geometry of Γ......Page 112 3.3. The Main Result......Page 113 4.1. On Generalizations......Page 115 4.2. On Applications......Page 116 References......Page 117 Summary......Page 119 References......Page 120 1. Setting of the Problem. Lieb-Thirring bounds......Page 122 2. Sharp Lieb-Thirring constants......Page 123 4. Logarithmic Lieb-Thirring estimates......Page 125 5. Setting of the problem: Berezin-Li-Yau inequalities......Page 127 6. Pólya-Berezin-Lieb-Li-Yau bounds......Page 128 7. Pólya’s conjecture in the presence of magnetic field......Page 129 9. Melas’ bound......Page 130 10. Improved Berezin bounds with remainder terms of correct order......Page 131 11. A more geometric second term......Page 132 12. Improving Melas’ bound......Page 133 References......Page 134 QUANTUM ENTANGLEMENT IN RANDOM SYSTEMS......Page 137 PART B Topical Sessions......Page 139 Session in honour of Ari Laptev......Page 141 1. Introduction......Page 143 2. Isoperimetric inequalities for eigenvalues of the Laplacian......Page 144 3. Brézis–Nirenberg problem in Sn and Hn......Page 146 References......Page 148 1.1. Introduction......Page 150 1.3. Strategy of the proof......Page 152 2. Local asymptotics......Page 154 2.2. Straightening the boundary......Page 155 2.3. Local asymptotics in half-space......Page 156 3. Localization......Page 158 References......Page 159 1. Introduction......Page 160 2. Main results......Page 161 3. About some techniques used in the proof......Page 163 3.2. A virial-type result......Page 164 References......Page 165 1. Introduction......Page 167 2. Generalities......Page 169 3. Heuristics......Page 171 4. The model function, regular case......Page 173 6. Crossover from exponential to non-exponential decay laws......Page 174 The exponential regime......Page 175 The non-exponential regime......Page 176 References......Page 177 1. Introduction......Page 181 2. Lifshitz tail estimates......Page 184 3. Wegner estimate......Page 186 References......Page 187 CALOGERO-SUTHERLAND TYPE SYSTEMS AND CONFORMAL FIELD THEORY......Page 188 Spectral theory......Page 189 1. Two families of interpolation inequalities......Page 190 2. Existence of extremals......Page 191 3. Symmetry and symmetry breaking......Page 193 References......Page 194 1. The setting......Page 195 2. Basic ideas......Page 196 3. Results......Page 197 4. Discussion of the results......Page 199 References......Page 200 HOMOGENIZATION OF THE WAVEGUIDES WITH FREQUENT ALTERNATION BOUNDARY CONDITIONS......Page 202 ABSOLUTELY CONTINUOUS SPECTRUM FOR SUBSTITUTION TREES......Page 203 SPECTRAL PROPERTIES OF LEAKY STAR GRAPH......Page 204 ON THE SINGULAR BEHAVIOUR OF SPECTRAL DENSITY FOR SCHRÖDINGER OPERATORS WITH WIGNER-VON NEUMANN PERTURBATION......Page 205 SPECTRAL PROBLEMS AND QUANTUM FEATURES OF FLUID IN NANOTUBE......Page 206 ON THE EIGENVALUE PROBLEM FOR A PARTICULAR CLASS OF JACOBI MATRICES......Page 207 FRACTIONAL MOMENT METHOD FOR NON-MONOTONE MODELS......Page 208 Many body quantum systems......Page 210 1. Model......Page 211 2. Result......Page 213 References......Page 214 1. Introduction......Page 215 2. Model and analyticity of the ground state......Page 216 3. Expansions in the fine structure constant......Page 217 References......Page 219 1. Introduction......Page 220 2. Non–Adiabatic Transitions......Page 221 3. Comments about the Proof......Page 222 4. Generalizations......Page 223 References......Page 224 ON THE IONIZATION ENERGY OF THE SEMIRELATIVISTIC PAULI-FIERZ MODEL......Page 225 ROTATING ULTRACOLD DIPOLAR GASES......Page 226 Quantum chaos......Page 227 1. Introduction......Page 228 2. Numerical results and conclusions......Page 229 References......Page 232 1. Introduction......Page 233 2.1. Damped quantum mechanics......Page 234 2.2. Complex scaled scattering Hamiltonian and open dynamics......Page 235 3. Fractal Weyl laws......Page 236 3.1. Spectral gaps......Page 237 References......Page 238 MANY-PARTICLE SYSTEMS ON QUANTUM GRAPHS WITH SINGULAR INTERACTIONS......Page 239 INTEGRABLE THEORY OF QUANTUM TRANSPORT IN CHAOTIC CAVITIES......Page 240 Quantum field theory......Page 241 RENORMALISATION HOPF ALGEBRAS FOR GAUGE THEORIES AND BRST SYMMETRIES......Page 242 EXACT SOLUTION OF A 2 + 1 DIMENSIONAL INTERACTING FERMION MODEL......Page 243 INFRARED ASPECTS OF A MODEL OF QFT ON A STATIC SPACE TIME......Page 244 KREIN SPACES IN DE SITTER QUANTUM THEORIES......Page 245 Quantum information......Page 246 HOLOGRAPHIC QUANTUM STATES......Page 247 PERFECT STATE TRANSFER WITHIN NETWORKS OF ARBITRARY TOPOLOGY......Page 248 CONTROLLABILITY OF QUANTUM WALKS ON GRAPHS......Page 249 OPTIMAL PARAMETRIZATIONS OF ADIABATIC PATHS......Page 250 ASYMPTOTIC DYNAMICS OF QUANTUM SYSTEMS UNDER RANDOM UNITARY EVOLUTION......Page 251 MOLECULAR SOLUTION FOR THE SUBSET-SUM PROBLEM ON DNA-BASED QUANTUM COMPUTING......Page 252 OPTIMAL REPLICATION OF VON NEUMANN MEASUREMENTS......Page 253 UNCERTAINTY RELATIONS AND ENTANGLEMENT IN FERMION SYSTEMS......Page 254 Physics of social systems......Page 255 1. Introduction......Page 256 2. Morphological structure of an urban system......Page 257 2.1. Rural Area......Page 258 2.2. Suburban Area......Page 260 2.3. City Core......Page 261 3. Summary......Page 263 References......Page 265 1. Introduction......Page 266 2. Verification strategies......Page 267 3.1. Data aquisition and analysis......Page 268 3.3. Verification process for the Hermes project......Page 270 References......Page 271 1. Introduction......Page 272 2.1. Parameter variance in spheres......Page 273 3.1. Results......Page 274 References......Page 276 ELLIPTICAL VOLUME EXCLUSION OF PEDESTRIAN CROWD......Page 277 EMPLOYMENT, PRODUCTION AND CONSUMPTION MODEL: PATTERNS OF PHASE TRANSITION......Page 278 LIST OF REGISTERED PARTICIPANTS......Page 279 AUTHOR INDEX......Page 285 Relative entropies and entanglement monotones / Nilanjana Datta -- Binding, stability, and non-binding of multi-polaron systems / Rupert L. Frank [und weitere] -- Interacting electrons on the honeycomb lattice / Alessandro Giuliani -- Renormalization of Dirac's polarized vacuum / Mathieu Lewin -- Convergence results for thick graphs / Olaf Post -- Spectral properties of Wigner matrices / Benjamin Schlein -- Lieb-Robinson bounds and quasi-locality for the dynamics of many-body quantum systems / Roberts Sims -- Disorder-induced delocalization on tree graphs / Michael Aizenman, Simone Warzel -- Semiclassical spectral bounds and beyond / Timo Weidl -- The other plenary talks abstracts -- Session in honour of Ari Laptev. Ari Laptev at sixty. Spectral problems in spaces of constant curvature / Rafael D. Benguria. Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain / Rupert L. Frank, Leander Geisinger. On the energy of the minimizers of the Ginzburg-Landau functional for exterior magnetic fields between H[symbol] and H[symbol] / Bernard Helffer. Decay law for resonances produced by perturbation of unstable eigenvalues close to a threshold / Victor Dinu, Arne Jensen, Cheorghe Nenciu. Localization in random displacement model / Michael Loss, Gunther Stolz. Contributed talks -- Spectral theory. Extremal functions in some interpolation inequalities : symmetry, symmetry breaking and estimates of the best constants / Jean Dolbeault, Maria J. Esteban. Effective Hamiltonians for thin Dirichlet tubes with varying cross-section / Jonas Lampart, Stefan Teufel, Jakob Wachsmuth. Other talks -- Many body quantum sustems. Diffusion in Hamiltonian quantum systems / Wojciech De Roeck. Ground state properties in non-relativistic QED / David Hasler, Ira Herbst. Non-adiabatic transitions in a simple Born-Oppenheimer scattering system / George A. Hagedorn, Alain Joye. Contributed talks -- Quantum chaos. Relationship between chaos and thermalization in one-dimensional quantum many-body systems / Lea F. santos, Marcos Rigol. Quantized open chaotic systems / Stephane Nonnenmacher. Other talks -- Quantum field theory. Invited and contributed talks -- Quantum information. Invited and contributed talks -- Physics of social systems. Morphology of the land parcel mosaic : the key to understand the urbanization process / Marcin Fialkowski, Agnieszka Bitner, Robert Holyst. Reliability issues in the microscopic modelling of pedestrian movement / Bernhard Steffen, Armin Seyfried, Maik Boltes. Urban structure analysis / Daniel Vasata, Pavel Exner, Petr Seba. Contributed talks The volume collects papers from talks given at QMath11 — Mathematical Results in Quantum Physics, which was held in Hradec Králové, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Králové was no exception. This volume collects papers from talks given at QMath11 - Mathematical Results in Quantum Physics, which was held in Hradec Kralove, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Kralove was no exception The volume collects papers from talks given at QMath11 - Mathematical Results in Quantum Physics, which was held in Hradec Kralove, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Kralove was no exception