Decoherence: A Numerical Study

TL;DR

This paper numerically investigates quantum decoherence in a tripartite system involving a relativistic quantum field, a measuring device, and an environment, demonstrating the rapid evolution towards classicality through decoherence effects.

Contribution

It introduces a numerical approach to study quantum decoherence in a relativistic quantum field coupled with a measuring device and environment, using exact diagonalization.

Findings

Decoherence causes the density matrix to become nearly diagonal in pointer states.

Evidence of decoherence is observed despite computational limitations on system size.

The study provides insights into the dynamics of quantum-to-classical transition.

Abstract

We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativistic particles. We solve the Schr\"odinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear evidence of decoherence: after tracing out the environment, the density matrix describing the system and measuring device evolves quickly towards a matrix that is close to diagonal in a subspace of pointer states.