Quasinormal mode expansion and late-time behavior of leaking systems

  • Suen W
  • Young K
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The wave function of a particle escaping from a barrier, in general, would have its quasinormal modes, which decay like exp(-gamma-t/2), dominated by anomalous t(-a) terms at asymptotically late times. One implication of the existence of these anomalous terms is that the wave function cannot be expressed as a sum of quasinormal modes. We show that these anomalous terms are related to classical motion linking the initial point (x',t = 0) to the final point (x,t). We then show that when the potential is unbounded from below, such terms do not appear, and more importantly, for such potential, the time development of a wave function initially concentrated in the finite region can be expressed in terms of a summation over quasinormal modes.

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  • Wai Mo Suen

  • Kenneth Young

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