Long time deviation from exponential decay: non-integral power laws
Quantum Physics
2009-11-13 v1
Abstract
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.
Cite
@article{arxiv.0709.2685,
title = {Long time deviation from exponential decay: non-integral power laws},
author = {J. Martorell and J. G. Muga and D. W. L. Sprung},
journal= {arXiv preprint arXiv:0709.2685},
year = {2009}
}