Long time deviation from exponential decay: non-integral power laws

TL;DR

This paper investigates the long-time deviation from exponential decay in quantum systems, proposing a mechanism involving long-range potentials that explains non-integer power law decay exponents observed experimentally.

Contribution

It introduces a physical mechanism based on scattering from long-tailed potentials that accounts for continuous variation in power law decay exponents.

Findings

Long-range potentials can produce a continuous spectrum of decay exponents.

Inverse square potential relates potential strength to decay exponent.

System predictions are testable experimentally.

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.