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Combescure, Monique

Trapping of quantum particles for a class of time-periodic potentials. A semi-classical approach. (English) Zbl 0634.35062

Ann. Phys. 172, 210-225 (1986).
Summary: We study the time evolution for Schrödinger operators with time- periodic potentials when the classical equations of motion possess periodic orbits. We exhibit a class of time-periodic potentials such that for initial states suitably localized around these periodic orbits, then at the dominant order of the semi-classical approximation, the system is trapped forever at sufficiently large frequency. An estimation of the correction to the semi-classical approximation is given, which yields a minimum “trapping time” for these systems.

Cited in 2 Documents

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35J10 Schrödinger operator, Schrödinger equation

Keywords:

time evolution; Schrödinger operators; time-periodic potentials; semi- classical approximation; trapping time
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\textit{M. Combescure}, Ann. Phys. 172, 210--225 (1986; Zbl 0634.35062)

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