Non-Hermitian physics and master equations

2022/01/14 by Federico Roccati, G. Massimo Palma, Fabio Bagarello +1 · 1 voice · 12 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Classical mechanics #Density matrix #Hamiltonian (control theory) #Hermitian matrix #Lindblad equation #Markov process #Master equation #Mathematical optimization #Mathematical physics #Mathematics #Open quantum system #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical physics #Theoretical physics #quant-ph

paper · pdf · doi:10.1142/s1230161222500044

published in Open Systems & Information Dynamics 29(01) (World Scientific) · 10 pages, 7 figures. Submitted to the Special Issue of OSID in memoriam of Andrzej Kossakowski

arxiv created 2022/01/14 · openalex publication_date 2022/03/01 · openalex created_date 2022/05/05 · arxiv updated 2022/09/07 · openalex updated_date 2026/08/05

Abstract

A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.

Citations

• Quantum Theory for Mathematicians
• Must a Hamiltonian be Hermitian?
• Making sense of non-Hermitian Hamiltonians
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Robust light transport in non-Hermitian photonic lattices
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Exceptional topology of non-Hermitian systems
• Open Quantum Systems. An Introduction

Cited by

• Variational quantum simulation of many-body dissipative dynamics on a superconducting quantum processor
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Many-Body Perturbation Theory for Driven Dissipative Quasiparticle Flows and Fluctuations
• Non-stabilizerness as a Diagnostic of Criticality and Exceptional Points in Non-Hermitian Spin Chains
• Non-Hermitian Physics in Quantum Channels: Pseudo-Hermiticity, Spectrum Measurement and Application to Hamiltonian Parameter Estimation
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Non-equilibrium Dynamics of Three-Level Absorption Refrigerator at Third-Order Liouvillian Exceptional Points
• Lindbladian versus Postselected Non-Hermitian Topology
• Non-Hermitian topology and skin modes in the continuum via parametric processes
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Equilibrium Thermodynamics of Non-Hermitian Dirac Fermions: Caloric and Magnetic Responses
• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model

Discussions

• There seem to be two schools of thought regarding non-Hermitian Hamiltonians. This review by Roccati et al. is a good resource. The first approach recognizes that such non-Hermitian Hamiltonians can a [stackexchange, 6 points]

Related

• Making Non-Markovian master equations accessible with approximate environments
• Non-Hermitian formalism and nonlinear physics
• Exact non-Markovian master equations: a generalized derivation for Gaussian systems
• Master equation for open quantum systems: Zwanzig-Nakajima projection technique and the intrinsic bath dynamics
• CP conditions for GKSL-like master equations