Nonadiabaticity of Quantum harmonic oscillators

TL;DR

This paper introduces a new measure, ${\\mathcal{A}\!\! /}$, to quantify the nonadiabaticity in thermodynamic processes of quantum harmonic oscillators, using an invariant-based approach and exploring its thermodynamic implications.

Contribution

It proposes a novel, invariant-based measure of nonadiabaticity for quantum harmonic oscillators and integrates it into thermodynamic laws.

Findings

Defined a measurable nonadiabaticity quantity ${\mathcal{A}\!\! /}$.

Applied the measure to frequency-modulated quantum harmonic oscillators.

Discussed potential universality and applications of the method.

Abstract

We propose a quantity, ${\mathcal{A}\!\!\!/}$, as a measure describing the nonadiabaticity of a thermodynamic process. For this purpose, we use a schematic method to find the measure of the `degree of nonadiabaticity'. The method utilizes an `invariant' thermal state constructed from the Ermakov-Lewis-Riesenfeld invariant. Specifically, we study a frequency-modulated quantum harmonic oscillator as a thermodynamic system. Naturally, we write the first law of thermodynamics with ${\mathcal{A}\!\!\!/}$ as a measurable quantity. We discuss universality for the method and some possible applications.