Decoherence, wave function collapses and non-ordinary statistical mechanics

TL;DR

This paper explores how different statistical mechanics frameworks affect the relaxation behavior of a pointer system interacting with a spin, highlighting differences between ordinary and non-ordinary statistics in decoherence models.

Contribution

It introduces a toy model demonstrating how non-ordinary statistical mechanics alter relaxation dynamics in decoherence, contrasting with traditional exponential relaxation.

Findings

Ordinary statistical mechanics leads to exponential relaxation.

Non-ordinary statistics result in inverse power law relaxation.

Real collapses and entanglement produce similar relaxation in the model.

Abstract

We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation.