Non-Hermitian physics and master equations

2022/01/14 by Federico Roccati, G. Massimo Palma, Fabio Bagarello +1 · 1 voice · 8 citations
#quant-ph

paper · pdf · doi:10.1142/s1230161222500044

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.

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• 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

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]

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• 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