Long Time Behaviour of Classical and Quantum Systems : Proceedings of the Bologna Aptex International Conference, Bologna, Italy, 13-17 September 1999.

This book is centered on the two minicourses conducted by C Liverani (Rome) and J Sjoestrand (Paris) on the return to equilibrium in classical statistical mechanics and the location of quantum resonances via semiclassical analysis, respectively. The other contributions cover related topics of classi...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Graffi, Sandro
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore : World Scientific Publishing Company, 2001.
Colección:Series on concrete and applicable mathematics.
Temas:
Mathematical physics > Congresses.
Microlocal analysis > Congresses.
Quantum theory > Congresses.
Physique mathématique > Congrès.
Analyse microlocale > Congrès.
Théorie quantique > Congrès.
Mathematical physics
Microlocal analysis
Quantum theory
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Foreword; List of Participants; CONTENTS; Return to Equilibrium in Classical and Quantum Systems; 1. FIRST LECTURE; 2. SECOND LECTURE; 3. THIRD LECTURE; 4. FOURTH LECTURE; Quantum Resonances and Trapped Trajectories; 1 Introduction; 2 Definitions and first results; 3 FBI transform and upper bounds on the density of resonances; 4 Trace formulae and lower bounds on the density of resonances; 5 Resonances and a non-linear Schrodinger equation; Return to Thermal Equilibrium in Quantum Statistical Mechanics; 1. INTRODUCTION; 2. EQUILIBRIUM STATES AND DYNAMICS OF FINITE SYSTEMS
  • 3. EQUILIBRIUM STATES AND DYNAMICS OF INFINITE SYSTEMS4. EXAMPLE: FINITE QUANTUM SYSTEM; 5. EXAMPLE: FREE QUANTIZED ELECTROMAGNETIC FIELD IN THE ARAKI-WOODS REPRESENTATION; 6. EXAMPLE: CONFINED ELECTRON AND FREE QUANTIZED ELECTROMAGNETIC FIELD
  • NONINTERACTING; 7. CONFINED ELECTRON COUPLED TO THE QUANTIZED RADIATION FIELD
  • INTERACTING CASE; Small Oscillations in Some Nonlinear PDE's; 1 Introduction; 2 The finite dimensional case; 3 The infinite dimensional case: some known results; 4 A proof of Lyapunov center theorem: the finite dimensional case; 5 The resonant case
  • 6 A proof of the Lyapunov center theorem: the infinite dimensional case7 On the verification of the property y-NR; 8 Applications; The Semi-Classical Van-Vleck Formula. Application to the Aharonov-Bohm Effect; 1 Introduction; 2 Coherent states and quantum propagator; 3 Semi-classical approximation for the propagator; 4 The time-dependent Aharonov-Bohm Effect; Fractal Dimensions and Quantum Evolution Associated with Sparse Potential Jacobi Matrices; 1 Introduction; 2 The sparse barrier model and main results; 3 Pictures of quantum motion within sparse barriers; 4 Proof of Theorem 2
  • 5 Proof of Theorem 36 Conclusions; Infinite Step Billiards; 1 Introduction; 2 The model and the results; 3 Outline of the proofs; Semiclassical Expansion for the Thermodynamic Limit of the Ground State Energy of Kac's Operator; 1 Introduction; 2 One-parameter families of weighted standard functions; 3 WKB constructions; 4 A formal asymptotic expansion; 5 Estimates for the thermodynamic limit; Asymptotics of Scattering Poles for Two Strictly Convex Obstacles; 1. INTRODUCTION; 2. METHOD OF THE PROOF; 3. EXPRESSION OF BROKEN RAYS CONVERGING TO THE PERIODIC RAY; 4. SOLUTIONS OF FUNCTION EQUATIONS
  • 5. TAYLOR EXPANSION OF Tn(s+t o+r)Parabolic Dynamical Systems and Inducing; 1 Preliminaires; 2 Parabolic rational maps; QFT for Scalar Particles in External Fields on Riemannian Manifolds; 1 Introduction; 2 Invariant wave equations on Riemannnian manifolds; 3 Classical S-matrix; 4 Feynman's scattering amplitude; 5 Solvability of the equation AF = A + iAP_AF; 6 Quantum field theory in external forces; 7 Hilbert-Schmidt property on Riemannian manifolds; 8 Massless case; Existence and Born-Oppenheimer Asymptotics of the Total Scattering Cross-Section in Ion-Atom Collisions; I Introduction

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