Decoherence and thermalization of a pure quantum state in quantum field theory

TL;DR

This paper investigates the real-time evolution of a self-interacting quantum field, demonstrating how a pure state undergoes decoherence and thermalization, with classical statistical field theory effectively describing the decoherence process.

Contribution

It provides a complete solution to nonequilibrium quantum dynamics of an O(N) scalar field using a 1/N-expansion at next-to-leading order, including scattering and memory effects.

Findings

Pure quantum states lose coherence over time.

The reduced density matrix thermalizes at long times.

Decoherence physics aligns with classical statistical field theory.

Abstract

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N-expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. Restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, the system is described by an effective (reduced) density matrix which, unlike the full density matrix, has a nontrivial time evolution. In particular, starting from a pure quantum state, we observe the loss of putity/coherence and, on longer time scales, thermalization of the reduced density matrix. We point out that the physics of decoherence is well described by classical statistical field theory.