Embedding quantum systems with a non-conserved probability in classical environments

TL;DR

This paper develops a formalism to embed quantum systems with non-conserved probability into classical environments by taking a classical limit over heavy degrees of freedom, revealing additional dissipation effects.

Contribution

It introduces a method to model non-Hermitian quantum dynamics within a classical environment, bridging quantum non-unitary evolution and classical dissipation.

Findings

Demonstrates the formalism with a two-spin chain example

Shows classical environment induces additional dissipation

Extends non-Hermitian quantum dynamics to classical settings

Abstract

Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution. The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to harmonic oscillators, is considered in order to illustrate the formalism.