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Waves and particles in the Fermi accelerator model. Numerical simulation; Ondes et particules dans le modele de l`accelerateur de Fermi. Simulation numerique

Abstract

This thesis is devoted to a numerical study of the quantum dynamics of the Fermi accelerator which is classically chaotic: it is particle in a one dimensional box with a oscillating wall. First, we study the classical dynamics: we show that the time of impact of the particle with the moving wall and its energy in the wall frame are conjugated variables and that Poincare surface of sections in these variables are more understandable than the usual stroboscopic sections. Then, the quantum dynamics of this systems is studied by the means of two numerical methods. The first one is a generalization of the KKR method in the space-time; it is enough to solve an integral equation on the boundary of a space-time billiard. The second method is faster and is based on successive free propagations and kicks of potential. This allows us to obtain Floquet states which we can on one hand, compare to the classical dynamics with the help of Husimi distributions and on the other hand, study as a function of parameters of the system. This study leads us to nice illustrations of phenomenons such as spatial localizations of a wave packet in a vibrating well or tunnel  More>>
Authors:
Publication Date:
Jan 01, 1996
Product Type:
Thesis/Dissertation
Report Number:
ISN-96-02
Reference Number:
SCA: 661300; 661100; PA: AIX-27:052412; EDB-96:109802; NTS-96:019573; SN: 96001618425
Resource Relation:
Other Information: TH: These (D. es Sc.).; PBD: Jan 1996
Subject:
66 PHYSICS; FERMI RESONANCE; ACCELERATION; DYNAMICS; STOCHASTIC PROCESSES; WAVE PACKETS; ADIABATIC PROCESSES; CLASSICAL MECHANICS; ENERGY SPECTRA; FLOQUET FUNCTION; GREEN FUNCTION; HARMONIC OSCILLATORS; MATHEMATICAL MODELS; MECHANICAL VIBRATIONS; NUMERICAL ANALYSIS; PHASE SHIFT; PHASE SPACE; QUANTUM MECHANICS; SCHROEDINGER EQUATION; SINGLE-PARTICLE MODES; SPACE-TIME; TRAJECTORIES; TRANSPORT THEORY; TUNNEL EFFECT; WAVE PROPAGATION
OSTI ID:
252910
Research Organizations:
Grenoble-1 Univ., 38 (France). Inst. des Sciences Nucleaires
Country of Origin:
France
Language:
French
Other Identifying Numbers:
Other: ON: DE96629706; TRN: FR9602006052412
Availability:
INIS; OSTI as DE96629706
Submitting Site:
FRN
Size:
156 p.
Announcement Date:
Jul 23, 1996

Citation Formats

Meplan, O. Waves and particles in the Fermi accelerator model. Numerical simulation; Ondes et particules dans le modele de l`accelerateur de Fermi. Simulation numerique. France: N. p., 1996. Web.
Meplan, O. Waves and particles in the Fermi accelerator model. Numerical simulation; Ondes et particules dans le modele de l`accelerateur de Fermi. Simulation numerique. France.
Meplan, O. 1996. "Waves and particles in the Fermi accelerator model. Numerical simulation; Ondes et particules dans le modele de l`accelerateur de Fermi. Simulation numerique." France.
@misc{etde_252910,
title = {Waves and particles in the Fermi accelerator model. Numerical simulation; Ondes et particules dans le modele de l`accelerateur de Fermi. Simulation numerique}
author = {Meplan, O}
abstractNote = {This thesis is devoted to a numerical study of the quantum dynamics of the Fermi accelerator which is classically chaotic: it is particle in a one dimensional box with a oscillating wall. First, we study the classical dynamics: we show that the time of impact of the particle with the moving wall and its energy in the wall frame are conjugated variables and that Poincare surface of sections in these variables are more understandable than the usual stroboscopic sections. Then, the quantum dynamics of this systems is studied by the means of two numerical methods. The first one is a generalization of the KKR method in the space-time; it is enough to solve an integral equation on the boundary of a space-time billiard. The second method is faster and is based on successive free propagations and kicks of potential. This allows us to obtain Floquet states which we can on one hand, compare to the classical dynamics with the help of Husimi distributions and on the other hand, study as a function of parameters of the system. This study leads us to nice illustrations of phenomenons such as spatial localizations of a wave packet in a vibrating well or tunnel effects. In the adiabatic situation, we give a formula for quasi-energies which exhibits a phase term independent of states. In this regime, there exist some particular situations where the quasi-energy spectrum presents a total quasi-degeneracy. Then, the wave packet energy can increase significantly. This phenomenon is quite surprising for smooth motion of the wall. The third part deals with the evolution of a classical wave in the Fermi accelerator. Using generalized KKR method, we show a surprising phenomenon: in most of situations (so long as the wall motion is periodic), a wave is localized exponentially in the well and its energy increases in a geometric way. (author). 107 refs., 66 figs., 5 tabs. 2 appends.}
place = {France}
year = {1996}
month = {Jan}
}