Scale-free relaxation of a wave packet in a quantum well with power-law tails

TL;DR

This paper predicts and demonstrates a power-law decay in a quantum wave packet within a well with specific tail behavior, supported by analytical derivation and numerical simulations relevant to cold atom experiments.

Contribution

It introduces a simple quantum system with power-law tails that exhibits observable power-law decay, supported by analytical and numerical analysis.

Findings

Power-law decay observed in quantum wave packets with specific tail behavior

Analytical derivation of decay law from spectral properties

Numerical simulations confirm predictions for cold atom experiments

Abstract

We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.