Rate of parity violation from measure concentration

TL;DR

This paper uses geometric measure concentration and isoperimetric inequalities to analyze how parity violation causes one chirality's degrees of freedom to dominate over the other, with interpretations in statistical mechanics.

Contribution

It introduces a geometric approach based on measure concentration and isoperimetric inequalities to quantify parity violation effects in phase space.

Findings

Quantifies the rate of parity violation using geometric measure concentration.

Provides a statistical mechanics interpretation of the parity violation process.

Establishes a connection between isoperimetric inequalities and chirality dominance.

Abstract

We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. We rely on the measure concentration of a subset of a Euclidean cube which is controlled by an isoperimetric inequality. We provide an interpretation of this result in terms of ideas of Statistical Mechanics.