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

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

2002-07-11

arxiv.org/abs/quant-ph/0207067v3

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevA.68.022702

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.

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