The Quantization process for the Driven Quantum Well - Perturbative Expansion and the Classical Limit
Abstract
We consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case, namely, its non-self-adjointness. Using this expansion, we calculate the first order contribution to the cross section and the energy gain, and discuss their classical limit. In this limit the one-period energy gain converges to its classical analog - the classical local (momentum space) diffusion coefficient. Both the classical and quantum mechanical results are compared with numerical simulations.
Cite
@article{arxiv.cond-mat/9512003,
title = {The Quantization process for the Driven Quantum Well - Perturbative Expansion and the Classical Limit},
author = {Eli Eisenberg and Nadav Shnerb and Rachel Avigur},
journal= {arXiv preprint arXiv:cond-mat/9512003},
year = {2008}
}
Comments
The first figure is available only via FAX. It contains only a Poincrare map of the classical system (see text). It can be found also in our paper in the Jan. 96 volume of PRE. Most readers could do without it. However, please send us an e-mail massage with your FAX number if you're interested