TY - THES
TI - Waves and particles in the Fermi accelerator model. Numerical simulation; Ondes et particules dans le modele de l`accelerateur de Fermi. Simulation numerique
AB - 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.
AU - Meplan, O
KW - 66 PHYSICS
KW - FERMI RESONANCE
KW - ACCELERATION
KW - DYNAMICS
KW - STOCHASTIC PROCESSES
KW - WAVE PACKETS
KW - ADIABATIC PROCESSES
KW - CLASSICAL MECHANICS
KW - ENERGY SPECTRA
KW - FLOQUET FUNCTION
KW - GREEN FUNCTION
KW - HARMONIC OSCILLATORS
KW - MATHEMATICAL MODELS
KW - MECHANICAL VIBRATIONS
KW - NUMERICAL ANALYSIS
KW - PHASE SHIFT
KW - PHASE SPACE
KW - QUANTUM MECHANICS
KW - SCHROEDINGER EQUATION
KW - SINGLE-PARTICLE MODES
KW - SPACE-TIME
KW - TRAJECTORIES
KW - TRANSPORT THEORY
KW - TUNNEL EFFECT
KW - WAVE PROPAGATION
DO -
UR - https://www.osti.gov/etdeweb/servlets/purl/252910
PB -
CY - France
PY - 1996
DA - 1996-01-01
LA - French
J2 -
C1 - Grenoble-1 Univ., 38 (France). Inst. des Sciences Nucleaires
C2 -
ER -