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Long time behaviour of classical and quantum systems [[electronic resource] ] : proceedings of the Bologna APTEX International Conference : Bologna, Italy, 13-17 September 1999 / / editors, Sandro Graffi & André Martinez
| Long time behaviour of classical and quantum systems [[electronic resource] ] : proceedings of the Bologna APTEX International Conference : Bologna, Italy, 13-17 September 1999 / / editors, Sandro Graffi & André Martinez |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (299 p.) |
| Disciplina | 530.1 |
| Altri autori (Persone) |
GraffiS <1943-> (Sandro)
MartinezAndré |
| Collana | Series on concrete and applicable mathematics |
| Soggetto topico |
Mathematical physics
Microlocal analysis Quantum theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93453-4
9786611934538 981-279-459-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910454405403321 |
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Long time behaviour of classical and quantum systems [[electronic resource] ] : proceedings of the Bologna APTEX International Conference : Bologna, Italy, 13-17 September 1999 / / editors, Sandro Graffi & André Martinez
| Long time behaviour of classical and quantum systems [[electronic resource] ] : proceedings of the Bologna APTEX International Conference : Bologna, Italy, 13-17 September 1999 / / editors, Sandro Graffi & André Martinez |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (299 p.) |
| Disciplina | 530.1 |
| Altri autori (Persone) |
GraffiS <1943-> (Sandro)
MartinezAndré |
| Collana | Series on concrete and applicable mathematics |
| Soggetto topico |
Mathematical physics
Microlocal analysis Quantum theory |
| ISBN |
1-281-93453-4
9786611934538 981-279-459-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910782391003321 |
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||