One-particle approximation as a simple playground for irreversible quantum evolution

TL;DR

This paper explores how one-particle approximation simplifies the analysis of irreversible quantum evolution and entanglement, providing a clearer physical interpretation and easier computational methods for such systems.

Contribution

It demonstrates that one-particle approximation reduces complexity in calculating reduced density matrices and entanglement, and links Lindblad evolution to a Schrödinger equation with a dissipative generator.

Findings

Simplified calculation of reduced density matrices and entanglement.

Connection between Lindblad equations and Schrödinger equations with dissipative generators.

Physical interpretation of non-Hermitian Hamiltonians in one-particle systems.

Abstract

Both quantum information features and irreversible quantum evolution of the models arising in physical systems in one-particle approximation are discussed. It is shown that the calculation of the reduced density matrix and entanglement analysis are considerably simplified in this case. The irreversible quantum evolution described by Gorini--Kossakowski--Sudarshan--Lindblad equations in the one-particle approximation could be defined by a solution of a Shroedinger equation with a dissipative generator. It simplifies the solution of the initial equation on the one side and gives a physical interpretation of such a Shroedinger equation with non-Hermitian Hamiltonian on the other side.