An Adiabatic Theorem without a Gap Condition

TL;DR

This paper reviews classical and quantum adiabatic theorems and introduces a new quantum adiabatic theorem that does not require a spectral gap, broadening the theorem's applicability.

Contribution

It presents a novel quantum adiabatic theorem that relaxes the traditional gap condition, expanding the theoretical framework.

Findings

Theorem applicable without spectral gap

Broader conditions for adiabatic evolution

Enhanced understanding of quantum adiabatic processes

Abstract

The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.