arXiv subjects

Rachel Avigur

Publications and source records attributed to Rachel Avigur.

2 recordsLinked to original sources

arXiv1995

The Quantization process for the Driven Quantum Well - Perturbative Expansion and the Classical Limit

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.

cond-mat↗

arXiv1995

Traces of a Quantum Anti-Resonance in a Driven System

It has been previously shown, that classically chaotic kicked systems, whose unperturbed spectrum posseses one energy scale, admits a quantum anti-resonance (QAR) behavior. In this study we extend the conditions under which which this QAR occurs for the case of a two-sided kicked 1D infinite potential well. It is then shown by a perturbative argument that this QAR effects the behavior of the equivalent driven well, i.e., the number of periods needed to leave the initial state has a sharp peak around the QAR. We give a numerical evidence that the anti resonance persists even for large values of the perturbation parameter.

cond-mat↗