Mathematical Results In Quantum Physics: Proceedings of the QMath11 Conference

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