# Exact analytical non-Hermitian formulation of the time evolution of decay of one and two identical quantum particles

## TL;DR

This paper presents an exact analytical method for describing the decay dynamics of one and two identical noninteracting quantum particles using resonant states, revealing distinctive exponential and long-time decay behaviors.

## Contribution

It introduces a non-Hermitian analytical formulation for the time evolution of decay in identical quantum particles, including entangled states, with explicit long-time decay characteristics.

## Key findings

- Wave functions exhibit exponential decay and long-time inverse power decay regimes.
- Different decay behaviors are observed for single and entangled two-particle states.
- The approach provides exact solutions for decay dynamics in non-Hermitian quantum systems.

## Abstract

An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and nonescape probabilities for the initial state of a single particle and entangled symmetric and antisymmetric initial states of two identical particles evolve in a distinctive form along the exponential and long-time nonexponential decaying regimes. In particular, for the last regime, they exhibit different inverse power of time behaviors.