Revealing the physical structure of the general quantum master equation

TL;DR

This paper provides a new physical perspective on the general quantum master equation, revealing that quantum dynamics can be understood through free evolution, charge exchanges, and dephasing without additional assumptions.

Contribution

It introduces a novel structure of the Lindblad master equation based on physical processes, unifying various effects like strong coupling and non-Abelian interactions.

Findings

Quantum dynamics can be expressed via free evolution, charge exchange, and dephasing.

Strong coupling, particle exchange, and non-Abelian effects share a common physical origin.

Generalized Gibbs states include non-commutation terms previously overlooked.

Abstract

The Lindblad (GKLS) master equation, which represents the mathematical form for the general evolution of a density matrix, is a versatile and widely-used tool in open quantum systems. In contrast with the typical approach of imposing additional conditions on the system, such as weak coupling or energy conservation, we explore the structure of the equation with no assumptions. We demonstrate that general quantum dynamics can be expressed through a combination of free evolution, exchanges of some physical quantities (generalised charges), not necessarily commuting with the Hamiltonian, between the system and the bath, and pure dephasing. This result comprises a novel perspective on quantum master equations, employing physical processes as elemental parts. We use it to explore the dynamics and stationary states of a two-level system and show that strong coupling, particle exchange, and non-Abelian effects all share the same physical origin. Moreover, we demonstrate that the generalised Gibbs state for all three cases contains a non-commutation term, which has not been previously considered.