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.

arXiv comment10 pages, 7 figures. Submitted to the Special Issue of OSID in memoriam of Andrzej Kossakowski

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• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• How to design quantum-jump trajectories via distinct master equation representations
• 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
• Enhanced charging in open Rabi and Dicke quantum batteries