Open Quantum Systems with Kadanoff-Baym Equations

TL;DR

This paper develops and numerically solves the non-equilibrium Kadanoff-Baym equations for a one-dimensional open quantum system, demonstrating thermalization, decoherence, and spectral evolution of particles interacting with a heat bath.

Contribution

It formulates a novel approach to modeling open quantum systems using Kadanoff-Baym equations with elastic scatterings and provides numerical solutions illustrating thermalization and decoherence.

Findings

System particles equilibrate with the heat bath

Off-diagonal density matrix elements decohere over time

Spectral properties evolve during thermalization

Abstract

We study the temporal evolution of quantum mechanical fermionic particles exhibiting one bound state within a one-dimensional attractive square-well potential in a heat bath of bosonic particles. For this open quantum system we formulate the non-equilibrium Kadanoff-Baym equations for the system particles by taking the interactions to be elastic 2-2 scatterings with the heat-bath particles. The corresponding spatially imhomogeneous integro-differential equations for the one-particle Greens's function are solved numerically. We demonstrate how the system particles equilibrate and thermalize with the heat bath and how the off-diagonal elements of the density matrix, expressed in the one-particle energy eigenbasis, decohere, so that only the diagonal entries, i.e. the occupation numbers, survive. In addition, the time evolution of the (retarded) Green's function also determines the spectral properties of the various one-particle quantum states.