Long-time behavior of many-particle quantum decay

TL;DR

This paper investigates the long-time non-exponential decay behavior of many-particle quantum systems, revealing how interactions and quantum statistics influence decay rates and patterns, with exact modeling of tunneling decay dynamics.

Contribution

It provides a detailed analysis of how contact interactions and quantum statistics affect long-time decay, highlighting differences between bosonic and fermionic systems and applying exact models.

Findings

Fermionic decay follows a quadratic power-law in particle number.

Bosonic decay exhibits a linear power-law in particle number.

Faster decay in fermions is due to spatial anti-bunching and effective hard-core interactions.

Abstract

While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time non-exponential behavior of the non-escape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that whereas for non-interacting bosons the long-time decay follows a power-law with an exponent linear in the number of particles $\N$, the exponent becomes quadratic in $\N$ in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial anti-bunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.