Weak (non)conservation and stochastic dynamics of angular momentum

TL;DR

This paper investigates how weak violations of rotational symmetry affect angular momentum conservation in isolated many-particle systems, using stochastic modeling and numerical simulations to describe decay and fluctuations.

Contribution

It introduces a mesoscopic stochastic framework for angular momentum decay under weak symmetry violation, validated by simulations and parameter estimation.

Findings

Langevin and Fokker-Planck equations consistent with equilibrium when symmetry holds

Analytical model accurately predicts angular momentum decay and fluctuations

Parameter estimation from simulations provides insights into dissipative coefficients

Abstract

Angular momentum conservation influences equilibrium statistical mechanics, leading to a generalized microcanonical density for an isolated system and a generalized Gibbs density for a weakly coupled system. We study the stochastic decay of angular momentum due to weakly imperfect rotational symmetry of the external potential that confines the isolated many-particle system. We present a mesoscopic description of the system, deriving Langevin and Fokker-Planck equations, which are consistent with equilibrium statistical mechanics when rotational symmetry is maintained. When the symmetry is weakly violated, we formulate a coarse-grained stochastic differential equation governing the decay of total angular momentum over time. To validate our analytical predictions, we conduct numerical simulations of the microcanonical ensemble, an isolated system undergoing thermalization due to weak two-body interactions. Our coarse-grained Langevin equation accurately characterizes both the decay of the angular momentum and its fluctuations in a steady state. Furthermore, we estimate the parameters of our mesoscopic model directly from simulations, providing insights into the dissipative phenomenological coefficients, such as friction. More generally, this study contributes to a deeper understanding of the behavior of the integrals of motion when the corresponding symmetry is weakly violated.