A Fluctuation-Dissipation Structure of Quantum Dynamical Semigroups Reveals a Unique Internal Hamiltonian

TL;DR

This paper develops a refined fluctuation-dissipation framework for quantum dynamical semigroups, enabling the unique identification of a system's internal Hamiltonian by analyzing the invariant diffusion-dissipation structure.

Contribution

It introduces a universal principle that distinguishes coherent from incoherent dynamics, resolving ambiguities in Markovian master equations for finite-dimensional quantum systems.

Findings

The diffusion-dissipation structure is invariant under Lindblad symmetries.

The internal Hamiltonian is uniquely determined by this invariance.

Provides a method to objectively identify a system's energy structure.

Abstract

We refine a fluctuation-dissipation framework for quantum dynamical semigroups to resolve a long-standing ambiguity in Markovian master equations. For finite-dimensional systems, we prove that the underlying diffusion-dissipation structure - rooted in a classical Markov process analogy - is invariant under Lindblad generator symmetries. This invariance uniquely identifies the internal Hamiltonian. Our framework provides a universal principle for objectively distinguishing coherent from incoherent parts of the dynamics, enabling an unambiguous determination of a system's inherent energy structure.