Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

Abstract

The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both S(t) and P(t) asymptotically exhibit the same power-law decrease at long times, when the initial wave packet in momentum representation behaves as O(1) or O(k) at small momentum. On the other hand, if the integer m becomes greater than 1, S(t) and P(t) decrease in different power-laws at long times.

4 pages, 3 figures, Title and organization changed, however the results not changed, To appear in Phys. Rev. A

References in corpus (2)

• Asymptotic behaviour of the probability density in one dimension
• The various power decays of the survival probability at long times for free quantum particle

Cited by in corpus (7)

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• Particle escapes in an open quantum network via multiple leads
• Escape behaviour of a quantum particle in a loop coupled to a lead
• Quantum particle escape from a time-dependent confining potential