Time evolution of decay of two identical quantum particles

TL;DR

This paper derives an analytical solution for the decay over time of two identical non-interacting quantum particles within a finite potential, highlighting how initial states and quantum statistics influence decay behavior.

Contribution

It introduces a formalism using resonant states to analyze the time evolution of decay for symmetric and entangled quantum states, including the effects of the Pauli exclusion principle.

Findings

Wave function evolution differs in exponential and nonexponential regimes.

Initial state symmetry affects decay dynamics.

Pauli exclusion influences decay patterns.

Abstract

An analytical solution for the time evolution of decay of two identical non interacting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave function, and hence also the survival and nonescape probabilities, for factorized symmetric and entangled symmetric/antisymmetric initial states evolve in a distinctive form along the exponentially decaying and nonexponential regimes. Our findings show the influence of the Pauli exclusion principle on decay. We exemplify our results by solving exactly the s-wave delta shell potential model.