New trends in mathematical physics: selected contributions of the XVth International Congress on Mathematical Physics
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2009
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| 245 | 1 | 0 | |a New trends in mathematical physics |b selected contributions of the XVth International Congress on Mathematical Physics |c ed.: Vladas Sidoravicius |
| 264 | 1 | |a Berlin |b Springer |c 2009 | |
| 300 | |a XLII, 872 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics |v Congresses | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 2006 |z Rio de Janeiro |2 gnd-content | |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 2 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sidoravicius, Vladas |0 (DE-588)123889308 |4 edt | |
| 711 | 2 | |a International Congress on Mathematical Physics |n 15 |d 2006 |c Rio de Janeiro |j Sonstige |0 (DE-588)6527563-9 |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-90-481-2810-5 |
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Datensatz im Suchindex
| _version_ | 1804139393916600320 |
|---|---|
| adam_text | Titel: New trends in mathematical physics
Autor: Sidoravicius, Vladas
Jahr: 2009
Contents
Entropy of Eigenfunctions........................................ 1
Nalini Anantharaman, Herbert Koch and Stephane Nonnenmacher
1 Motivations.............................................. 1
2 Main Result.............................................. 4
3 Outline of the Proof....................................... 7
3.1 Definition of the Metric Entropy..................... 7
3.2 From Classical to Quantum Dynamical Entropy........ 9
3.3 Entropic Uncertainty Principle....................... 13
3.4 Applying the Entropic Uncertainty Principle to the
Laplacian Eigenstates.............................. 14
References............................................... 21
Stability of Doubly Warped Product Spacetimes ..................... 23
Lars Andersson
1 Introduction.............................................. 23
2 Warped Product Spacetimes ................................ 24
2.1 Asymptotic Behavior.............................. 26
3 Fuchsian Method ......................................... 27
3.1 Velocity Dominated Equations....................... 28
3.2 Velocity Dominated Solution........................ 29
4 Stability................................................. 30
References............................................... 31
Rigorous Construction of Luttinger Liquids Through Ward Identities ... 33
Giuseppe Benfatto
1 Introduction.............................................. 33
2 The Tomonaga Model with Infrared Cutoff.................... 34
3 The RG Analysis.......................................... 35
4 The Dyson Equation....................................... 37
5 The First Ward Identity.................................... 39
6 The Second Ward Identity.................................. 40
xxviii Contents
7 The Euclidean Thirring Model.............................. 41
References............................................... 43
New Algebraic Aspects of Perturbative and Non-perturbative Quantum
Field Theory ................................................... 45
Christoph Bergbauer and Dirk Kreimer
1 Introduction.............................................. 45
2 Lie and Hopf Algebras of Feynman Graphs ................... 46
3 From Hochschild Cohomology to Physics..................... 50
4 Dyson-Schwinger Equations................................ 51
5 Feynman Integrals and Periods of Mixed (Tate) Hodge
Structures................................................ 55
References............................................... 57
Exact Solution of the Six-Vertex Model with Domain Wall Boundary
Conditions..................................................... 59
Pavel M. Bleher
1 Six-Vertex Model......................................... 59
2 Phase Diagram of the Six-Vertex Model ...................... 62
3 Izergin-Korepin Determinantal Formula...................... 63
4 The Six-Vertex Model with DWBC and a Random Matrix
Model................................................... 63
5 Asymptotic Formula for the Recurrence Coefficients............ 65
6 Previous Exact Results..................................... 67
7 Zinn-Justin s Conjecture................................... 70
8 Large N Asymptotics of Z# in the Ferroelectric Phase.......... 71
References............................................... 71
Mathematical Issues in Loop Quantum Cosmology................... 73
Martin Bojowald
1 Introduction.............................................. 73
2 Quantum Representation and Dynamical Equations............. 75
2.1 Quantum Reduction ............................... 75
2.2 Dynamics........................................ 76
3 Quantum Singularity Problem............................... 78
4 Examples for Properties of Solutions......................... 79
5 Effective Theory.......................................... 81
6 Summary................................................ 84
References............................................... 84
Boundary Effects on the Interface Dynamics for the Stochastic
Allen-Cahn Equation............................................ 87
Lorenzo Bertini, Stella Brassesco and Paolo Butta
1 Introduction.............................................. 87
2 Results and Strategy of Proofs .............................. 89
References............................................... 92
Contents xxjx
Dimensional Entropies and Semi-Uniform Hyperbolicity.............. 95
Jerome Buzzi
1 Introduction.............................................. 95
2 Low Dimension........................................... 97
2.1 Interval Maps..................................... 97
2.2 Surface Transformations............................ 98
3 Dimensional Entropies..................................... 99
3.1 Singular Disks.................................... 99
3.2 Entropy of Collections of Subsets....................100
3.3 Definitions of the Dimensional Entropies..............101
4 Other Growth Rates of Submanifolds.........................102
4.1 Volume Growth...................................102
4.2 Resolution Entropies...............................106
5 Properties of Dimensional Entropies......................... 107
5.1 Link between Topological and Resolution Entropies .... 107
5.2 Gap Between Uniform and Ordinary Dimensional
Entropies ........................................108
5.3 Continuity Properties ..............................109
6 Hyperbolicity from Entropies...............................110
6.1 A Ruelle-Newhouse Type Inequality .................110
6.2 Entropy-Expanding Maps...........................110
6.3 Entropy-Hyperbolicity.............................112
6.4 Examples of Entropy-Hyperbolic Diffeomorphisms.....113
7 Further Directions and Questions............................113
7.1 Variational Principles..............................113
7.2 Dimensional Entropies of Examples..................113
7.3 Other Types of Dimensional Complexity..............114
7.4 Necessity of Topological Assumptions................114
7.5 Entropy-Hyperbolicity.............................114
7.6 Generalized Entropy-Hyperbolicity ..................115
8 C Sizes.................................................115
References...............................................116
The Scaling Limit of (Near-)Critical 2D Percolation .................. 117
Federico Camia
1 Introduction..............................................117
1.1 Critical Scaling Limits and SLE.....................117
1.2 Percolation.......................................120
2 The Critical Loop Process..................................121
2.1 General Features.................................. 121
2.2 Construction of a Single Loop....................... 122
3 The Near-Critical Scaling Limit............................. 124
References............................................... 125
xxx Contents
Black Hole Entropy Function and Duality........................... I27
Gabriel Lopes Cardoso
1 Introduction..............................................1^7
2 Entropy Function and Electric/Magnetic Duality Covariance.....128
3 Application to N = 2 Supergravity ..........................130
4 Duality Invariant OSV Integral..............................133
References...............................................133
Weak Turbulence for Periodic NLS ................................ 135
James Colliander
1 Introduction..............................................135
2 NLS as an Infinite System of ODEs..........................137
3 Conditions on a Finite Set A c Z2 ..........................138
4 Arnold Diffusion for the Toy Model ODE.....................139
5 Construction of the Resonant Set A..........................140
References...............................................142
Angular Momentum-Mass Inequality for Axisymmetric Black Holes----- 143
Sergio Dain
1 Introduction..............................................143
2 Variational Principle for the Mass............................144
References...............................................147
Almost Everything About the Fibonacci Operator.................... 149
David Damanik
1 Introduction..............................................149
2 The Trace Map...........................................150
3 The Cantor Structure and the Dimension of the Spectrum........152
4 The Spectral Type.........................................154
5 Bounds on Wavepacket Spreading...........................156
References...............................................158
Entanglement-Assisted Quantum Error-Correcting Codes............. 161
Igor Devetak, Todd A. Brun and Min-Hsiu Hsieh
1 Introduction..............................................161
2 Notations................................................162
3 Entanglement-Assisted Quantum Error-Correcting Codes........163
3.1 The Channel Model: Discretization of Errors ..........164
3.2 The Entanglement-Assisted Canonical Code...........165
3.3 The General Case .................................167
3.4 Distance.........................................169
3.5 Generalized F4 Construction........................169
3.6 Bounds on Performance............................170
4 Conclusions..............................................171
References...............................................171
Contents xxxi
Particle Decay in Ising Field Theory with Magnetic Field.............. 173
Gesualdo Delfino
1 Ising Field Theory ........................................173
2 Evolution of the Mass Spectrum.............................175
3 Particle Decay off the Critical Isotherm.......................176
4 Unstable Particles in Finite Volume..........................182
References...............................................184
Fluctuations and Large Deviations in Non-equilibrium Systems........ 187
Bernard Derrida
1 Introduction..............................................187
2 Large Deviation Function of the Density......................188
3 Free Energy Functional....................................189
4 Simple Exclusion Processes (SSEP)..........................191
5 The Large Deviation Function (p(x)) for the SSEP...........193
6 The Matrix Ansatz for the Symmetric Exclusion Process........194
7 Additivity as a Consequence of the Matrix Ansatz..............197
8 Large Deviation Function of Density Profiles..................198
9 Non-locality of the Large Deviation Functional of the Density
and Long Range Correlations...............................200
10 The Macroscopic Fluctuation Theory.........................202
11 Large Deviation of the Current..............................203
12 Generalized Detailed Balance and the Fluctuation Theorem......204
13 Current Fluctuations in the SSEP............................206
14 The Additivity Principle....................................207
References...............................................209
Robust Heterodimensional Cycles and Tame Dynamics................ 211
Lorenzo J. Diaz
1 Robust Heterodimensional Cycles ...........................211
1.1 General Setting...................................211
1.2 Basic Definitions..................................213
1.3 Robust Cycles at Heterodimensional Cycles...........214
1.4 Questions and Consequences........................216
2 Cycles and Non-hyperbolic Tame Dynamics...................217
2.1 Setting ..........................................217
2.2 Tangencies, Heterodimensional Cycles, and Examples... 218
3 Robust Homoclinic Tangencies, Non-dominated Dynamics, and
Heterodimensional Cycles..................................220
4 Ingredients of the Proof of Theorem 2........................222
4.1 Strong Homoclinic Intersections of Saddle-Nodes......223
4.2 Model Blenders___ ...............................225
References...............................................227
xxxii Contents
Hamiltonian Perturbations of Hyperbolic PDEs: from Classification
Results to the Properties of Solutions............................... 231
Boris Dubrovin
1 Introduction..............................................231
2 Towards Classification of Hamiltonian PDEs..................235
3 Deformation Theory of Integrable Hierarchies.................238
4 Frobenius Manifolds and Integrable Hierarchies
of the Topological Type....................................249
5 Critical Behaviour in Hamiltonian PDEs, the Dispersionless
Case....................................................264
6 Universality in Hamiltonian PDEs...........................269
References...............................................273
Lattice Supersymmetry from the Ground Up........................ 277
Paul Fendley and Kareljan Schoutens
References...............................................284
Convergence of Symmetric Trap Models in the Hypercube............. 285
L.R.G. Fontes and P.H.S. Lima
1 Introduction..............................................285
1.1 The Model.......................................286
2 Convergence to the K Process...............................287
2.1 Proof of Theorem 1................................288
3 The REM-Like Trap Model and the Random Hopping Times
Dynamics for the REM ....................................294
3.1 The REM-Like Trap Model.........................294
3.2 Random Hopping Times Dynamics for the REM.......295
References...............................................296
Spontaneous Replica Symmetry Breaking in the Mean Field Spin Glass
Model......................................................... 299
Francesco Guerra
1 Introduction..............................................299
2 The Mean Field Spin Glass Model. Basic Definitions...........302
3 The Thermodynamic Limit.................................304
4 The Parisi Representation for the Free Energy .................305
5 Conclusion and Outlook for Future Developments..............309
References...............................................310
Surface Operators and Knot Homologies........................... 313
Sergei Gukov
1 Introduction..............................................313
2 Gauge Theory and Categorification..........................316
2.1 Incorporating Surface Operators.....................318
2.2 Braid Group Actions...............................320
Contents xxxiii
3 Surface Operators and Knot Homologies in .jY = 2 Gauge
Theory..................................................323
3.1 Donaldson-Witten Theory and the Equivariant Knot
Signature ........................................323
3.2 Seiberg-Witten Theory.............................326
4 Surface Operators and Knot Homologies in «yK = 4 Gauge
Theory..................................................330
References...............................................340
Conformal Field Theory and Operator Algebras..................... 345
Yasuyuki Kawahigashi
1 Introduction..............................................345
2 Conformal Quantum Field Theory...........................346
3 Representation Theory.....................................349
4 Classification Theory......................................350
5 Moonshine Conjecture.....................................352
References...............................................354
Diffusion and Mixing in Fluid Flow: A Review....................... 357
Alexander Kiselev
1 Introduction..............................................357
2 The Heart of the Matter....................................363
3 Open Questions...........................................367
References...............................................368
Random Schrodinger Operators: Localization and Delocalization, and
All That....................................................... 371
Francois Germinet and Abel Klein
1 Random Schrodinger Operators.............................371
2 Basic Examples of Random Schrodinger Operators.............372
2.1 The Anderson (Tight-Binding) Model ................373
2.2 The (Continuum) Anderson Hamiltonian..............373
2.3 The Random Landau Hamiltonian....................373
2.4 The Poisson Hamiltonian...........................374
3 The Metal-Insulator Transition..............................374
4 The Spectra] Metal-Insulator Transition.......................375
4.1 Anderson Localization.............................375
4.2 Absolutely Continuous Spectrum....................377
4.3 The Spectral Metal-Insulator Transition
for the Anderson Model on the Bethe Lattice..........377
5 The Dynamical Metal-Insulator Transition....................378
5.1 Dynamical Localization............................378
5.2 Transport Exponents...............................379
5.3 The Dynamical Spectral Regions ....................380
5.4 The Region of Complete Localization ................381
xxxiv Contents
6 The Dynamical Transition in the Random Landau Hamiltonian ... 382
References...............................................384
Unifying R-Symmetry in M-Theory................................ 389
Axel Kleinschmidt
1 Introduction..............................................389
2 Kinematics...............................................392
2.1 Definition of eio and K(e o) ........................392
2.2 Level Decompositions for D = 11, IIA and IIB ........393
2.3 Representations of K(t o)..........................394
3 Dynamics................................................396
4 Discussion...............................................398
4.1 Remarks.........................................398
4.2 Outlook..........................................399
References...............................................400
Stable Maps are Dense in Dimensional One ......................... 403
Oleg Kozlovski, and Sebastian van Strien
1 Introduction..............................................403
2 Density of Hyperbolicity...................................404
3 Quasi-Conformal Rigidity..................................405
4 How to Prove Rigidity?....................................405
4.1 The Strategy of the Proof of QC-Rigidity..............406
5 Enhanced Nest Construction................................407
6 Small Distortion of Thin Annuli.............................409
7 Approximating Non-renormalizable Complex Polynomials......411
References...............................................412
Large Gap Asymptotics for Random Matrices.......................413
Igor Krasovsky
References...............................................419
On the Derivation of Fourier s Law................................ 421
Antti Kupiainen
1 Introduction..............................................421
2 Coupled Oscillators .......................................422
3 Closure Equations.........................................424
4 Kinetic Limit.............................................427
References...............................................431
Noncommutative Manifolds and Quantum Groups...................433
Giovanni Landi
1 Introduction..............................................433
2 The Algebras and the Representations........................435
2.1 The Algebras of Functions and of Symmetries.........435
2.2 The Equivariant Representation of s/(SUq{2)).........438
2.3 The Spin Representation............................439
Contents xxxv
3 The Equivariant Dirac Operator.............................442
4 The Real Structure........................................444
4.1 The Tomita Operator of the Regular Representation.....444
4.2 The Real Structure on Spinors.......................445
5 The Local Index Formula for SUq{2).........................447
5.1 The Cosphere Bundle and the Dimension Spectrum.....448
5.2 The Local Index Formula for 3-Dimensional
Geometries.......................................450
5.3 The Pairing Between HCX and ^i...................452
References...............................................454
Topological Strings on Local Curves ............................... 457
Marcos Marino
1 Introduction..............................................457
2 Topological Strings on Local Curves.........................459
2.1 A Model.........................................459
2.2 Relation to Hurwitz Theory.........................460
2.3 Mirror Symmetry from Large Partitions...............462
2.4 Higher Genus and Matrix Models....................464
3 Phase Transitions, Critical Behavior and Double-Scaling Limit ... 465
3.1 Review of Phase Transitions in Topological String
Theory..........................................465
3.2 Phase Transitions for Local Curves...................467
4 Non-perturbative Effects and Large Order Behavior.............469
References...............................................472
Repeated Interaction Quantum Systems............................ 475
Marco Merkli
1 Introduction..............................................475
2 Deterministic Systems.....................................477
2.1 Mathematical Description ..........................477
2.2 Results..........................................481
2.3 Asymptotic State..................................481
2.4 Correlations Reconstruction of Initial State..........482
3 Random Systems .........................................482
3.1 Dynamics and Random Matrix Products ..............482
3.2 Results...........................................484
4 An Example: Spins........................................486
5 Some Proofs .............................................490
References...............................................494
String-Localized Quantum Fields, Modular Localization, and Gauge
Theories....................................................... 495
Jens Mund
1 The Notion of String-Localized Quantum Fields...............495
xxxvi Contents
2 Modular Localization and the Construction of Free
String-Localized Fields....................................497
3 Results on Free String-Localized Fields.......................499
3.1 Fields and Two-Point Functions .....................499
3.2 Feynman Propagators..............................503
4 Outlook: Interacting String-Localized Fields...................504
References...............................................507
Kinks and Particles in Non-integrable Quantum Field Theories........ 509
Giuseppe Mussardo
1 Introduction..............................................509
2 A Semiclassical Formula...................................513
3 Symmetric Wells..........................................515
4 Asymmetric Wells ........................................519
5 Conclusions..............................................522
References...............................................523
Exponential Decay Laws in Perturbation Theory of Threshold
and Embedded Eigenvalues....................................... 525
Arne Jensen and Gheorghe Nenciu
1 Introduction..............................................525
2 The Basic Formula........................................528
3 The Results..............................................530
3.1 Properly Embedded Eigenvalues.....................530
3.2 Threshold Eigenvalues.............................531
4 A Uniqueness Result......................................533
5 Examples................................................534
5.1 Example 1: One Channel Case, v = — 1 ..............534
5.2 Example 2: Two Channel Case, v = -1, 1 ............535
5.3 Example 3: Two Channel Radial Case, v 3..........536
References...............................................537
Energy Diffusion and Superdiffusion in Oscillators Lattice Networks___ 539
Stefano Olla
1 Introduction..............................................539
2 Conservative Stochastic Dynamics...........................541
3 Diffusive Evolution: Green-Kubo Formula....................544
4 Kinetic Limits: Phonon Boltzmann Equation..................545
5 Levy s Superdiffusion of Energy.............................546
References...............................................546
Trying to Characterize Robust and Generic Dynamics................ 549
Enrique R. Pujals
1 Introduction..............................................549
2 Robust Transitivity: Hyperbolicity, Partial Hyperbolicity
and Dominated Splitting ...................................551
Contents xxxvii
2.1 Hyperbolicity.....................................553
2.2 Partial Hyperbolicity...............................554
2.3 Dominated Splitting...............................555
2.4 A General Question About Weak Form
of Hyperbolicity ..................................557
2.5 Robust Transitivity and Mechanisms:
Heterodimensional Cycle...........................557
3 Wild Dynamics...........................................558
3.1 Wild Dynamic and Homoclinic Tangency.............558
3.2 Surfaces Diffeomorphisms and Beyond...............559
4 Generic Dynamics: Mechanisms and Phenomenas..............560
References...............................................561
Dynamics of Bose-Einstein Condensates............................ 565
Benjamin Schlein
1 Introduction..............................................565
2 Heuristic Derivation of the Gross-Pitaevskii Equation...........567
3 Main Results.............................................571
4 General Strategy of the Proof and Previous Results.............574
5 Convergence to the Infinite Hierarchy........................576
6 Uniqueness of the Solution to the Infinite Hierarchy............580
6.1 Higher Order Energy Estimates......................581
6.2 Expansion in Feynman Graphs ......................583
References...............................................589
Locality Estimates for Quantum Spin Systems....................... 591
Bruno Nachtergaele and Robert Sims
1 Introduction..............................................591
2 Lieb-Robinson Bounds.....................................593
3 Quasi-Locality of the Dynamics.............................598
4 Exponential Clustering.....................................601
5 The Lieb-Schultz-Mattis Theorem...........................604
5.1 The Result and Some Words on the Proof.............605
5.2 A More Detailed Outline of the Proof.................607
References...............................................614
On Resolvent Identities in Gaussian Ensembles at the Edge
of the Spectrum................................................. 615
Alexander Soshnikov
1 Introduction..............................................615
2 Proof of Theorems 1 and 3 .................................622
3 Proof of Theorems 4 and 5 .................................624
4 Non-Gaussian Case .......................................625
References...............................................626
xxxviii Contents
Energy Current Correlations for Weakly Anharmonic Lattices 629
Herbert Spohn
1 Introduction..............................................629
2 Anharmonic Lattice Dynamics..............................630
3 Energy Current Correlations................................633
4 The Linearized Collision Operator...........................637
5 Gaussian Fluctuation Theory................................639
References...............................................640
Metastates, Translation Ergodicity, and Simplicity of Thermodynamic
States in Disordered Systems: an Illustration........................ 643
Charles M. Newman and Daniel L. Stein
1 Introduction..............................................643
2 The Sherrington-Kirkpatrick Model and the Parisi Replica
Symmetry Breaking Solution ...............................644
3 Open Problems...........................................645
4 Metastates...............................................645
5 Invariance and Ergodicity ..................................646
6 A Strategy for Rigorous Studies of Spin Glasses ...............647
7 Summary................................................651
References...............................................651
Random Matrices, Non-intersecting Random Walks, and Some Aspects
of Universality.................................................. 653
Toufic M. Suidan
1 Introduction..............................................653
1.1 Selected Basic Facts from Random Matrix Theory......654
1.2 The Karlin-McGregor Formula......................654
2 The Models..............................................655
2.1 Longest Increasing Subsequence of a Random
Permutation......................................655
2.2 ABC-Hexagon....................................657
2.3 Last Passage Percolation ...........................657
2.4 Non-intersecting Brownian Motion...................660
3 Universality..............................................661
3.1 Last Passage Percolation ...........................662
3.2 Non-intersecting Random Walks.....................662
References...............................................664
Homogenization of Periodic Differential Operators as a Spectral
Threshold Effect................................................ 667
Mikhail S. Birman and Tatiana A. Suslina
1 Introduction..............................................667
2 Periodic DO s. The Effective Matrix.........................668
3 Homogenization of Periodic DO s. Principal Term
of Approximation for the Resolvent..........................670
Contents xxxix
4 More Accurate Approximation for the Resolvent
in the L2-Operator Norm...................................671
5 (L2 - H )-Approximation of the Resolvent. Approximation
of the Fluxes in Li........................................673
6 The Method of Investigation................................674
7 Some Applications........................................678
8 On Further Development of the Method ......................681
References...............................................682
ABCD and ODEs ............................................... 685
Patrick Dorey, Clare Dunning, Davide Masoero, Junji Suzuki and
Roberto Tateo
1 Introduction..............................................685
2 Bethe Ansatz for Classical Lie Algebras......................688
3 The Pseudo-Differential Equations...........................689
4 Conclusions..............................................693
References...............................................694
Nonrational Conformal Field Theory............................... 697
J6rg Teschner
1 Introduction..............................................697
2 Constraints from Conformal Symmetry.......................699
2.1 Motivation: Chiral Factorization of Physical Correlation
Functions........................................699
2.2 Vertex Algebras...................................700
2.3 Representations of Vertex Algebras ..................701
2.4 Conformal Blocks.................................701
2.5 Correlation Functions vs. Hermitian Forms............703
3 Behavior Near the Boundary of Moduli Space.................704
3.1 Gluing of Riemann Surfaces ........................705
3.2 Gluing of Conformal Blocks........................708
3.3 Correlation Functions..............................710
3.4 Conformal Blocks as Matrix Elements................712
4 From one Boundary to Another..............................713
4.1 The Modular Groupoid.............................714
4.2 Representation of the Generators on Spaces
of Conformal Blocks...............................717
4.3 Representation of the Relations on Spaces of Conformal
Blocks...........................................718
5 Notion of a Stable Modular Functor..........................719
5.1 Towers of Representations of the Modular Groupoid .... 719
5.2 Unitary Modular Functors..........................721
5.3 Similarity of Modular Functors......................722
5.4 Friedan-Shenker Modular Geometry..................722
6 Example of a Nonrational Modular Functor...................723
xj Contents
6.1 Unitary Positive Energy Representations of the Virasoro
Algebra..........................................724
6.2 Construction of Virasoro Conformal Blocks in Genus
Zero.............................................725
6.3 Factorization Property..............................726
6.4 The Hilbert Space Structure.........................727
6.5 Extension to Higher Genus..........................728
6.6 Remarks.........................................729
7 Existence of a Canonical Scalar Product?.....................729
7.1 Existence of a Canonical Hermitian Form
from the Factorization Property......................730
7.2 Unitary Fusion....................................732
7.3 Associativity of Unitary Fusion......................733
7.4 Discussion.......................................735
8 Outlook.................................................735
8.1 Modular Functors from W-algebras and Langlands
Duality..........................................735
8.2 Boundary CFT....................................736
8.3 Nonrational Verlinde Formula?......................736
References...............................................738
Kinetically Constrained Models................................... 741
Nicoletta Cancrini, Fabio Martinelli, Cyril Roberto and Cristina Toninelli
References...............................................751
The Distributions of Random Matrix Theory and their Applications .... 753
Craig A. Tracy and Harold Widom
1 Random Matrix Models: Gaussian Ensembles.................753
1.1 Largest Eigenvalue Distributions Fp. Painleve II
Representations...................................754
1.2 Next-Largest, Next-Next Largest, Etc. Eigenvalue
Distributions .....................................757
2 Universality Theorems.....................................757
2.1 Invariant Ensembles...............................757
2.2 Wigner Ensembles.................................759
3 Multivariate Statistical Analysis.............................759
3.1 Principal Component Analysis (PCA) ................760
3.2 Testing the Null Hypothesis.........................760
3.3 Spiked Populations: BBP Phase Transition............761
4 Conclusions..............................................763
References...............................................763
Hybrid Formalism and Topological Amplitudes...................... 767
Jiirg Kappeli and Stefan Theisen and Pierre Vanhove
1 Introduction..............................................767
2 Compactified String Theory in RNS and Hybrid Variables.......768
Contents xli
2.1 Hybrid Variables..................................768
2.2 RNS Variables....................................772
2.3 Field Redefinition from RNS to Hybrid Variables.......773
2.4 Physical State Conditions and J^ = 4-embeddings.....776
2.5 Massless Vertex Operators..........................778
3 Amplitudes and Correlation Functions........................780
3.1 Amplitudes.......................................780
3.2 Correlation Functions of Chiral Bosons...............782
4 Topological Amplitudes....................................783
4.1 Generalities......................................783
4.2 tf-charge (g - 1, g - 1)............................784
4.3 /^-charge (1 - g, 1 - g)............................785
4.4 /^-charges (g - 1, 1 - g) and (1 - g, g - 1)...........787
4.5 Summary of the Amplitude Computation..............788
A Appendix: Conventions and Notations........................789
A. 1 Spinors and Superspace............................789
A.2 Hybrid Variables and JV = 2 Algebra................790
A.3 The Integrated Vertex Operator......................791
B Appendix: Mapping the RNS to the Hybrid Variables...........792
B. 1 Field Redefinition from RNS to Chiral GS Variables___792
B.2 Similarity Transformation Relating Chiral GS
to Hybrid Variables................................792
B.3 Hermitian Conjugation of the Hybrid Variables.........793
B.4 Hermitian Conjugation of the RNS Variables ..........794
C Appendix: Vertex Operators ................................797
C.I Massless RNS Vertex Operators.....................797
C.2 Universal Massless Multiplets.......................799
C.3 Compactification Dependent Massless Multiplets.......799
References...............................................802
Quantum Phases of Cold Bosons in an Optical Lattice ................ 805
Michael Aizenman, Elliot H. Lieb, Robert Seiringer, Jan Philip Solovej and
Jakob Yngvason
1 Introduction..............................................806
2 Reflection Positivity.......................................810
3 Proof of BEC for Small X. and T.............................811
4 Absence of BEC and Mott Insulator Phase....................816
5 The Non-interacting Gas...................................820
6 Conclusion...............................................821
References...............................................821
Random Walks in Random Environments in the Perturbative Regime ... 823
Ofer Zeitouni
1 Introduction..............................................823
2 Local Limits for Exit Measures..............................825
References...............................................826
xlji Contents
Appendix: Complete List of Abstracts.............................. 827
YRS and XV ICMP
1 Young Researchers Symposium Plenary Lectures ..............827
2 XV International Congress on Mathematical Physics Plenary
Lectures.................................................830
3 XV International Congress on Mathematical Physics Specialized
Sessions.................................................835
3.1 Condensed Matter Physics..........................835
3.2 Dynamical Systems................................836
3.3 Equilibrium Statistical Mechanics....................839
3.4 Non-equilibrium Statistical Mechanics................840
3.5 Exactly Solvable Systems...........................843
3.6 General Relativity.................................844
3.7 Operator Algebras.................................846
3.8 Partial Differential Equations........................847
3.9 Probability Theory ................................849
3.10 Quantum Mechanics...............................850
3.11 Quantum Field Theory.............................852
3.12 2D Quantum Field Theory..........................854
3.13 Quantum Information..............................855
3.14 Random Matrices .................................858
3.15 Stochastic PDE...................................860
3.16 String Theory.....................................861
Index.......................................................... 865
|
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| discipline | Physik Germanistik / Niederlandistik / Skandinavistik Mathematik |
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| spelling | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics ed.: Vladas Sidoravicius Berlin Springer 2009 XLII, 872 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik Mathematical physics Congresses Dynamisches System (DE-588)4013396-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2006 Rio de Janeiro gnd-content Differentialgleichung (DE-588)4012249-9 s Dynamisches System (DE-588)4013396-5 s Mathematische Physik (DE-588)4037952-8 s DE-604 Sidoravicius, Vladas (DE-588)123889308 edt International Congress on Mathematical Physics 15 2006 Rio de Janeiro Sonstige (DE-588)6527563-9 oth Erscheint auch als Online-Ausgabe 978-90-481-2810-5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017739320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics Mathematische Physik Mathematical physics Congresses Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4012249-9 (DE-588)4037952-8 (DE-588)1071861417 |
| title | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics |
| title_auth | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics |
| title_exact_search | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics |
| title_full | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics ed.: Vladas Sidoravicius |
| title_fullStr | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics ed.: Vladas Sidoravicius |
| title_full_unstemmed | New trends in mathematical physics selected contributions of the XVth International Congress on Mathematical Physics ed.: Vladas Sidoravicius |
| title_short | New trends in mathematical physics |
| title_sort | new trends in mathematical physics selected contributions of the xvth international congress on mathematical physics |
| title_sub | selected contributions of the XVth International Congress on Mathematical Physics |
| topic | Mathematische Physik Mathematical physics Congresses Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Mathematical physics Congresses Dynamisches System Differentialgleichung Konferenzschrift 2006 Rio de Janeiro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017739320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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