指数衰减的长时间偏差：非整数幂律
Long time deviation from exponential decay: non-integral power laws
摘要：
量子系统被预测在很长的时间内表现出从指数衰减到幂律衰减的转变。尽管大多数理论研究预测整数幂律指数，但Rothe等人最近对溶液中有机分子的衰变发光的测量（Phys.Rev.Lett. 96（2006）163601}在大多数情况下发现非整数指数。我们提出了一个物理机制，在从长尾巴的潜力，它产生了一个连续的范围内的幂律指数的散射领域。在易处理的情况下，排斥平方反比势，我们证明了一个简单的关系的强度之间的长程尾和幂律指数。这个系统经得起实验检验。
英文摘要：
Quantal systems are predicted to show a change-over from exponential decay to power law decay at very long times. Although most theoretical studies predict integer power-law exponents, recent measurements by Rothe et al. of decay luminescence of organic molecules in solution {Phys. Rev. Lett. 96 (2006) 163601} found non-integer exponents in most cases. We propose a physical mechanism, within the realm of scattering from potentials with long tails, which produces a continuous range of power law exponents. In the tractable case of the repulsive inverse square potential, we demonstrate a simple relation between the strength of the long range tail and the power law exponent. This system is amenable to experimental scrutiny.
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