Generating shortcuts to adiabaticity in quantum and classical dynamics

TL;DR

This paper introduces a unified framework for transitionless quantum driving and its classical analogue, providing exact expressions for counter-diabatic terms in specific systems and generalizing to power-law potentials.

Contribution

It formulates a classical analogue of quantum transitionless driving using a generator of adiabatic transport, extending the concept to classical systems and general potentials.

Findings

Exact expressions for counter-diabatic terms in single-particle piston.

Unified classical and quantum framework for adiabatic shortcuts.

Generalization to even-power-law potentials.

Abstract

Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counter-diabatic Hamiltonian to stifle non-adiabatic transitions. Here this strategy is cast in terms of a generator of adiabatic transport, leading to a classical analogue: dissipationless classical driving. For the single-particle piston, this approach yields simple and exact expressions for both the classical and quantal counter-diabatic terms. These results are further generalized to even-power-law potentials in one degree of freedom.