On adiabatic evolution for a general time-dependent quantum system

TL;DR

This paper derives a quantum invariant operator for adiabatic open systems, constructs a revised adiabatic theorem, and connects it to Berry's theorem, enhancing understanding of quantum evolution under adiabatic conditions.

Contribution

It introduces a new approach to analyze adiabatic evolution in general quantum systems using unitary transformations and quantum invariants.

Findings

Derived the quantum invariant operator from classical canonical transformations.

Constructed a revised adiabatic theorem applicable to open systems.

Showed the new theorem reduces to Berry's theorem in special cases.

Abstract

The unitary operator corresponding to the classical canonical transformation that connects a general closed system to an open system under adiabatic conditions is found. The quantum invariant operator of the adiabatic open system is derived from the unitary transformation of the quantum Hamiltonian of the closed system. On the basis of these results, we investigate the evolution of the general quantum adiabatic system and construct a revised adiabatic theorem. The adiabatic theorem developed here exactly reduces to the well-known Berry adiabatic theorem when the control parameter