A new method for directly computing reduced density matrices

TL;DR

This paper introduces a first-principles, non-Markovian method for directly computing reduced density matrices of open quantum systems using quantum field theory techniques, avoiding master equations.

Contribution

It presents a novel perturbative approach based on quantum field theory methods for calculating reduced density matrices without relying on master equations or the Markov approximation.

Findings

Derived a general formula for perturbative density matrix elements

Applied the method to a scalar field toy model

Demonstrated the approach's effectiveness in a simple example

Abstract

We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is based on techniques from non-equilibrium quantum field theory like thermo field dynamics, the Schwinger-Keldsyh formalism, and the Feynman-Vernon influence functional. It does not require the Markov approximation and is essentially a Lehmann-Szymanzik-Zimmermann-like reduction. In order to illustrate this method, we consider a real scalar field as an open quantum system interacting with an environment comprising another real scalar field. We give a general formula that allows for the perturbative computation of density matrix elements for any number of particles in a momentum basis. Finally, we consider a simple toy model and use this formula to obtain expressions for some of the system's reduced density matrix elements.