Long Tail of Quantum Decay from Scattering Data

TL;DR

This paper proposes a semi-empirical method to analyze the long-time decay tail of unstable quantum systems using scattering data, connecting spectral functions to phase shifts and density of states.

Contribution

It introduces a novel approach to determine the long-time decay behavior of quantum systems directly from scattering data, addressing a gap in experimental and theoretical understanding.

Findings

Connects survival probability to scattering phase shifts.

Provides a semi-empirical method to extract long-time decay from data.

Establishes the spectral function as proportional to the density of states.

Abstract

Whereas the short time behaviour of an unstable quantum mechanical system is well understood from its theoretical as well as experimental side, the long time tail of the very same systems has neither been measured experimentally nor is there a theoretical agreement on how to handle it. We suggest a possible way out of this unsatisfactory state of art. Theoretically we suggest that the correct spectral function entering the Fock-Krylov method to calculate the survival amplitude is proportional to the density of states of a resonance. The latter is essentially the energy derivative of a phase shift. As a bonus, we can connect the survival probability to scattering data via the phase shift. The method then not only establishes the spectral function, but is per se a semi-empirical method to extract the large time behaviour from scattering data.