Dynamical fluctuations in classical adiabatic processes: General description and their implications

TL;DR

This paper derives a general description of intrinsic dynamical fluctuations in classical adiabatic processes and explores their implications for geometric phases and phase objects like Hannay's angle.

Contribution

It introduces a comprehensive theoretical framework for understanding dynamical fluctuations in classical adiabatic systems, extending the classical adiabatic theorem.

Findings

Reveals the existence of an adiabatic geometric phase in certain dynamical models.

Discusses potential disturbances to Hannay's angle caused by dynamical fluctuations.

Provides a general formula describing intrinsic fluctuations in classical adiabatic processes.

Abstract

Dynamical fluctuations in classical adiabatic processes are not considered by the conventional classical adiabatic theorem. In this work a general result is derived to describe the intrinsic dynamical fluctuations in classical adiabatic processes. Interesting implications of our general result are discussed via two subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model with an adiabatically moving fixed-point solution, and the possible "pollution" to Hannay's angle or to other adiabatic phase objects for adiabatic processes involving non-fixed-point solutions.