## Abstract

We investigate the survival probability of a localized 1D quantum particle subjected to a time-dependent potential of the form rU(x) sin ωt with U(x) = 2δ(x - a) or U(x) = 2δ(x - a) - 2δ(x + a). The particle is initially in a bound state produced by the binding potential -2δ(x). We prove that this probability goes to zero as t → ∞ for almost all values of r, ω and a. The decay is initially exponential followed by a t^{-3} law if ω is not close to resonances and r is small; otherwise the exponential disappears and Fermi's golden rule fails. For exceptional sets of parameters r, ω and a the survival probability never decays to zero, corresponding to the Floquet operator having a bound state. We show similar behaviour even in the absence of a binding potential: permitting a free particle to be trapped by harmonically oscillating delta function potential.

Original language | English (US) |
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Pages (from-to) | 8943-8951 |

Number of pages | 9 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 42 |

DOIs | |

State | Published - Oct 25 2002 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)