Classical and Quantum Correlation Functions for a Ring Model

TL;DR

This paper derives classical and quantum correlation functions for particles on a ring, showing how classical decay behavior emerges from quantum expressions in the limit of Planck's constant approaching zero.

Contribution

It provides a detailed derivation of correlation functions for a ring model and clarifies the classical-quantum correspondence in their behavior.

Findings

Classical correlation functions exhibit decay over time.

Quantum correlation functions are strictly periodic.

Classical decay behavior can be obtained from quantum expressions as Planck's constant approaches zero.

Abstract

Classical and quantum correlation functions are derived for a system of non-interacting particles moving on a circle. It is shown that the decaying behaviour of the classical expression for the correlation function can be recovered from the strictly periodic quantum mechanical expression by taking the limit that the Planck's constant goes to zero, after an appropriate transformation.