Time evolution for quantum systems at finite temperature

TL;DR

This paper introduces a non-perturbative, fully quantized formalism for describing real-time evolution in finite-temperature quantum systems, validated through numerical tests on harmonic oscillators and tunneling phenomena.

Contribution

It presents a novel formalism for finite-temperature quantum dynamics that enables probabilistic interpretation and is applicable to complex systems and field theories.

Findings

Numerical methods effectively compute path integrals in complex time.

Results agree with exact solutions for harmonic oscillators.

Short-time distributions propagate causally in relativistic cases.

Abstract

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check selfconsistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable.