A new method for directly computing reduced density matrices

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.

27 pages, 15 figures, as published in PRD

References in corpus (15)

• Gravitational Decoherence
• Open Quantum Systems for Quarkonia
• Bottomonium production in heavy-ion collisions using quantum trajectories: Differential observables and momentum anisotropy
• Quantum simulation of open quantum systems in heavy-ion collisions
• Non-Abelian Electric Field Correlator at NLO for Dark Matter Relic Abundance and Quarkonium Transport
• Quarkonium Semiclassical Transport in Quark-Gluon Plasma: Factorization and Quantum Correction
• Gravitational Decoherence: A Thematic Overview
• Gravitational decoherence of photons
• Quantum Hotspots: Mean Fields, Open EFTs, Nonlocality and Decoherence Near Black Holes
• Field-theoretical approach to open quantum systems and the Lindblad equation
• Qubit Heating Near a Hotspot
• Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation
• Decoherence in an Interacting Quantum Field Theory: Thermal Case
• Gravitational decoherence: a non relativistic spin 1/2 fermionic model
• Bottomonium observables in an open quantum system using the quantum trajectories method

Cited by in corpus (12)

• Dilaton-induced open quantum dynamics
• In-in formalism for the entropy of quantum fields in curved spacetimes
• An Open Effective Field Theory for light in a medium
• Density matrix formalism for interacting quantum fields
• Search for dark energy with neutron interferometry
• Frequency shifts induced by light scalar fields
• Open system dynamics in interacting quantum field theories
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Effective field theory of particle mixing
• Reduced Density Matrices and Phase-Space Distributions in Thermofield Dynamics
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Particles in finite volumes and a toy model of decaying neutrons