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

MARC

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245 1 0 |a Long Time Behaviour of Classical and Quantum Systems :  |b Proceedings of the Bologna Aptex International Conference, Bologna, Italy, 13-17 September 1999. 
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520 |a 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 classical and quantum mechanics, such as scattering theory, classical and quantum statistical mechanics, dynamical localization, quantum chaos, ergodic theory and KAM techniques. Contents: Return to Equilibrium in Classical and Quantum Systems (C Liverani); Quantum Resonances and Trapped Trajectories (J S. 
505 0 |a 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 
505 8 |a 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 
505 8 |a 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 
505 8 |a 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 
505 8 |a 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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650 0 |a Mathematical physics  |v Congresses. 
650 0 |a Microlocal analysis  |v Congresses. 
650 0 |a Quantum theory  |v Congresses. 
650 6 |a Physique mathématique  |v Congrès. 
650 6 |a Analyse microlocale  |v Congrès. 
650 6 |a Théorie quantique  |v Congrès. 
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650 7 |a Microlocal analysis  |2 fast 
650 7 |a Quantum theory  |2 fast 
655 7 |a Conference papers and proceedings  |2 fast 
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