Transition to the continuum of a particle in time-periodic potentials. (English) Zbl 1041.81013
Karpeshina, Yulia (ed.) et al., Advances in differential equations and mathematical physics. Proceedings of the 9th UAB international conference, University of Alabama, Birmingham, AL, USA, March 26–30, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3296-4). Contemp. Math. 327, 75-86 (2003).
Summary: We present new results for the transition to the continuum of an initially bound quantum particle subject to a harmonic forcing. Using rigorous exponential asymptotics methods we obtain explicit expressions, as generalized Borel summable transseries, for the probability of localization in a specified spatial region at time \(t\). The transition to the continuum occurs for general compactly supported potentials in one dimension and our results extend easily to higher dimensional systems with spherical symmetry. This of course implies the absence of discrete spectrum of the corresponding Floquet operator.
For the entire collection see [Zbl 1015.00019].
For the entire collection see [Zbl 1015.00019].
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
