Abstract
We study the evolution of the energy distribution for a stadium with moving walls. We consider a one period driving cycle, which is characterized by an amplitude A and a wall velocity V. This evolving energy distribution has both "parametric" and "stochastic" components. The latter are important for the theory of quantum irreversibility and dissipation in driven mesoscopic devices. For an extremely slow wall velocity V, the spreading mechanism is dominated by transitions between neighboring levels, while for larger (nonadiabatic) velocities, the spreading mechanism has both perturbative and nonperturbative features. We present a numerical study which is aimed at identifying the latter features. A procedure is developed for the determination of the various V regimes. The possible implications of linear response theory are discussed.
Highlights
Consider the problem of a particle in a box, where some piece of the wall is deformed periodically in time
We study the evolution of the energy distribution for a stadium with moving walls
We consider a one period driving cycle, which is characterized by an amplitude A and a wall velocity V. This evolving energy distribution has both ‘‘parametric’’ and ‘‘stochastic’’ components. The latter are important for the theory of quantum irreversibility and dissipation in driven mesoscopic devices
Summary
Consider the problem of a particle in a box, where some piece of the wall is deformed periodically in time. We are going to study what happens to a quantum-mechanical particle in such a box, during one cycle of the driving. The problem of a particle in a box with a moving wall is a prototype example for study of driven systems1͔ which are described by a Hamiltonian H„x(t)..., where x(t) is a time dependent parameter. As a result of the driving, stochastic energy spreading of a relatively simple nature1͔. This is the case that we want to consider in this paper. Thanks to a new powerful technique for finding clusters of billiard eigenstates7,10,11͔ Previous applications of this technique, to the study of restricted aspects of the present problem, have been reported in Refs. This allows the identification of the various V regimes‘‘adiabatic,’’ ‘‘perturbative,’’ ‘‘nonperturbative,’’ and ‘‘sudden’’͒, which were predicted in past theoretical studies
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