Decay modes of two repulsively interacting bosons

TL;DR

This paper investigates how two repulsively interacting bosons decay by tunneling through a barrier, analyzing different particle presence regions and decay modes using numerical solutions of the Schrödinger equation.

Contribution

It provides a detailed numerical analysis of decay mechanisms of two interacting bosons, including decay rates and dominant modes, with predictions from boundary conditions and simple models.

Findings

In-in decay is exponential and well-predicted by boundary conditions.

In-out decay is dominated by single-particle decay for certain interaction strengths.

Decay mechanisms are effectively described by simple models.

Abstract

We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle presence: both particles inside the trap (in-in), one particle in and one particle out (in-out), and both particles outside (out-out). It is shown that the in-in probability is dominated by exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength the decay of in-out probability is dominated by the single particle decay mode. The decay mechanisms are adequately described by simple models.