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

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.

References in corpus (7)

• Renormalization of the Inverse Square Potential
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Cited by in corpus (9)

• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Amplification of non-Markovian decay due to bound state absorption into continuum
• Enhanced observability of quantum post-exponential decay using distant detectors
• Quantum decay and amplification in a non-Hermitian unstable continuum
• Resonant spectra of quadrupolar anions
• Bound and resonance states of the dipolar anion of hydrogen cyanide: competition between threshold effects and rotation in an open quantum system
• Scale-free relaxation of a wave packet in a quantum well with power-law tails
• Classical picture of post-exponential decay
• Memory effects induced by initial switching conditions