# 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.

## Key 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.