Amplification of non-Markovian decay due to bound state absorption into continuum

Authors

  • S. Garmon,

    Corresponding author
    1. Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
    • Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
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    • Phone: +1 416 946 7466, Fax: +1 416 978 8775

  • T. Petrosky,

    1. Center for Complex Quantum Systems, University of Texas at Austin, 1 University Station, C1609, Austin, Texas 78712, USA
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  • L. Simine,

    1. Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
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  • D. Segal

    1. Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
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Abstract

It is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time ‘near zone’ and long time ‘far zone’. In the near zone the survival probability falls off according to a t-1 power law, and in the far zone i t falls off as t-3. We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t-1 power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t-1 power law dominates precisely at the point of ejection.

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