Invariant Perturbation Theory of Adiabatic Process

TL;DR

This paper introduces an invariant perturbation theory for adiabatic processes, utilizing concepts like adiabatic orbits and U(1)-invariance, with calculations of orbit retention probabilities and a practical sufficient condition.

Contribution

It develops a novel invariant perturbation framework for adiabatic processes, including higher-order probability calculations and a new sufficient condition.

Findings

First-order and second-order adiabatic orbit retention probabilities calculated.

A convenient sufficient condition for adiabatic invariance provided.

Framework based on U(1)-invariant adiabatic orbits.

Abstract

In this paper we present an invariant perturbation theory to adiabatic process according to the concepts of adiabatic orbits, adiabatic evolution orbit and U(1)-invariant adiabatic orbit. The probabilities of keeping the adiabatic orbit in the first-order and the second-order approximation are calculated, respectively. We also give a convenient sufficient condition.