Non-Hermitian physics and master equations

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.

10 pages, 7 figures. Submitted to the Special Issue of OSID in memoriam of Andrzej Kossakowski

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Quantum collision models: open system dynamics from repeated interactions
• Quantum master equation with balanced gain and loss
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Cited by in corpus (8)

• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Quantum battery with non-Hermitian charging
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• Quantum correlations in dissipative gain-loss systems across exceptional points
• Practical quantum simulation of small-scale non-Hermitian dynamics
• Mixedness timescale in non-Hermitian quantum systems
• Nonlocal pseudospin dynamics in a quantum Ising chain