Dynamics of "Classical" Bosons, Fermions, and beyond

TL;DR

This paper explores the classical dynamics of particles with quantum statistical properties, revealing how exchange statistics influence their trajectories and behavior in various potentials, bridging classical and quantum descriptions.

Contribution

It introduces a classical framework reflecting quantum exchange statistics through symplectic geometry, extending understanding of quantum-classical correspondence for particles with quantum statistics.

Findings

Classical analogues of quantum exclusion and bunching behaviors identified.

Exchange statistics influence particle trajectories in quadratic potentials.

Comparison with quantum simulations highlights the classical model's insights.

Abstract

We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective classical manifold associated with two-particle bosonic and fermionic coherent states, we show how their exchange statistics is reflected in the symplectic form of the manifold. We demonstrate the classical analogues of exclusion or bunching behavior expected in such states by studying their trajectories in various quadratic potentials. Our examples are two-particle coherent states in one dimension and two-particle vortex motion in the lowest Landau level. We finally compare and contrast our results with previous simulations of the full quantum system, and with existing results on the geometric interpretations of quantum mechanics.