Nonequilibrium Thermo Field Dynamics Using 4x4-Matrix Transformation for System with Bose--Einstein Condensation

TL;DR

This paper develops a nonequilibrium theoretical framework for Bose--Einstein condensates using Thermo Field Dynamics and a 4x4 matrix transformation, deriving quantum transport equations through self-energy analysis.

Contribution

It introduces a general 4x4 transformation approach within Thermo Field Dynamics to describe nonequilibrium Bose--Einstein condensates with spontaneous symmetry breaking.

Findings

Derived quantum transport equations for normal and anomalous distributions.

Established a renormalization condition ensuring self-energy vanishes on-shell.

Formulated a comprehensive unperturbed Hamiltonian for the system.

Abstract

This study aims to construct a theoretical formulation of a nonequilibrium process for a system of Bose--Einstein condensate associated with a spontaneous symmetry breakdown. For this, Thermo Field Dynamics is used. We then describe the most general forms of a 4x4 transformation and an unperturbed Hamiltonian. After calculating the $4\times 4$ self-energy and identifying its on-shell, we impose the renormalization condition in which the entire on-shell self-energy should vanish. This condition provides a sufficient number of independent equations to determine all of the parameters in an unperturbed Hamiltonian, among which the quantum transport equations for normal and anomalous number distributions are included.