Resonant-state expansions and the long-time behavior of quantum decay
Resonant-state expansions and the long-time behavior of quantum decay
复制标题
共振态膨胀和量子衰变的长期行为
DOI：
10.1103/physreva.76.012103
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发表时间：
2007
影响因子：
2.9
通讯作者：
J. Villavicencio
中科院分区：
文献类型：
--
作者：
G. García;I. Maldonado;J. Villavicencio
结果表明，衰变波函数的共振和加非指数积分项的表示可以写成纯离散的共振和，方法是用最陡下降法对积分项进行长时间求值，然后用共振态展开所得的表达式。这导致了在时间区域中沿着指数幂和反指数幂有效的表示。通过模型计算，我们可以比较展开式和数值积分在连续波函数方面的差异，以及在长时间内，用最陡下降法得到的积分项的精确解析表达式。结果表明，共振态对衰变的长时间行为给出了正确的描述。
It is shown that a representation of the decaying wave function as a resonant sum plus a nonexponential integral term may be written as a purely discrete resonant sum by evaluating at long times the integral term by the steepest descents method, and then expanding the resulting expression in terms of resonant states. This leads to a representation that is valid along the exponential and the inverse power in time regimes. A model calculation using the $\ensuremath{\delta}$ potential allows us to make a comparison of the expansion with numerical integrations in terms of continuum wave functions and, in the long time regime, with an exact analytic expression of the integral term obtained using the steepest descents method. The results demonstrate that resonant states give a correct description of the long-time behavior of decay.