Long time behaviour of classical and quantum systems : proceedings of the Bologna APTEX International Conference : Bologna, Italy, 13-17 September 1999 / editors, Sandro Graffi & Andre Martinez.

Format:

Book

Conference/Event

Author/Creator:

Bologna APTEX International Conference, Corporate Author.

Contributor:

Graffi, S. (Sandro), 1943-

Martinez, André.

Conference Name:

Bologna APTEX International Conference (1999 : Bologna, Italy)

Bologna APTEX International Conference

Series:

Series on concrete and applicable mathematics ; 1.

Series on concrete and applicable mathematics ; 1

Language:

English

Subjects (All):

Mathematical physics--Congresses.

Mathematical physics.

Microlocal analysis--Congresses.

Microlocal analysis.

Quantum theory--Congresses.

Quantum theory.

Physical Description:

1 online resource (299 p.)

Edition:

1st ed.

Other Title:

Long time behavior of classical and quantum systems

Bologna APTEX International Conference

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c2001.

Language Note:

English

Summary:

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

Contents:

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

II Notation assumptions and main results

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611934538

9781281934536

1281934534

9789812794598

981279459X

OCLC:

879023737