Analysis of resonant population transfer in time-dependent elliptical quantum billiards

Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jan;87(1):012912. doi: 10.1103/PhysRevE.87.012912. Epub 2013 Jan 22.

Abstract

A Fermi golden rule for population transfer between instantaneous eigenstates of elliptical quantum billiards with oscillating boundaries is derived. Thereby the occurrence of both the recently observed resonant population transfer between instantaneous eigenstates and the empirical criterion stating that these transitions occur when the driving frequency matches the mean difference of the latter [Lenz et al., New J. Phys. 13, 103019 (2011)] is explained. As a second main result a criterion judging which resonances are resolvable in a corresponding experiment of certain duration is provided. Our analysis is complemented by numerical simulations for three different driving laws. The corresponding resonance spectra are in agreement with the predictions of both criteria.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computer Simulation
  • Models, Statistical*
  • Quantum Theory*