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

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.

► General result of fluctuations around idealized adiabatic orbits. ► New classical geometric angle arising from dynamical fluctuations. ► Pollution to Hannay’s angle for non-fixed-point solutions. ► Pollution to adiabatic phase in nonlinear Schrödinger equation.