Dynamical phase transition for a quantum particle source

TL;DR

This paper investigates the long-term behavior of quantum particle sources, revealing conditions for different growth regimes and establishing a semiclassical limit, with distinctions between bosonic and fermionic particles.

Contribution

It provides spectral criteria for growth behaviors and analyzes the local convergence and semiclassical limit of the density matrix in quantum sources.

Findings

Fermionic sources exhibit sublinear or linear growth based on spectral properties.

Bosonic sources can show exponential growth under certain conditions.

The paper establishes the semiclassical limit for the quantum source dynamics.

Abstract

We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for sublinear or linear growth in the fermionic case, but also establishing the possibility of exponential growth for bosons. We further study the local convergence of the density matrix in the long time limit and prove the semiclassical limit.