Dynamical invariant formalism of shortcuts to adiabaticity

TL;DR

This paper introduces the dynamical invariant formalism as a pedagogical approach to designing shortcuts to adiabaticity, linking it to counterdiabatic methods and illustrating with examples like Lax pairs and flow equations.

Contribution

It presents a clear, educational framework for using dynamical invariants to achieve adiabatic-like quantum dynamics, connecting various existing methods.

Findings

Provides a formalism for designing Hamiltonian coefficients using dynamical invariants.

Demonstrates the relation between dynamical invariants and counterdiabatic driving.

Illustrates the approach with examples such as Lax pairs and flow equations.

Abstract

We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to realize adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone, and flow equation.