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arXiv:1710.05993 · Open Systems & Information Dynamics

A Brief History of the GKLS Equation

Dariusz Chruściński, Saverio Pascazio

Published Sep 1, 2017• 202 citations
arXivHTMLPDF

Abstract

We reconstruct the chain of events, intuitions and ideas that led to the formulation of the Gorini, Kossakowski, Lindblad and Sudarshan equation.
DOI
10.1142/s1230161217400017

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Abstract We present an alternative derivation of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation based on complex Riccati equations and the associated dynamical invariants. Our formulation introduces time-dependent coefficients, which satisfy the constraints imposed by the Robertson-Schrödinger uncertainty relations, as previously discussed by Dekker et al. in the time-independent case. This time dependence may provide new insights and perspectives for extending the framework to non-Markovian systems.
The year 2026 marks the fiftieth anniversary of the two seminal papers in which Gorini, Kossakowski, and Sudarshan, and independently Lindblad, characterized the generators of completely positive quantum dynamical semigroups. We revisit the conceptual and historical route leading to the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation and examine several of its early developments and consequences. Our aim is to show how several initially separate mathematical and physical ideas converged in the GKLS structure theorem, imme- diately opening the way to manifold consequences for the description of dissipative quantum phenomena and how that theorem, fifty years later, remains both a foundational result and an active framework for open quantum dynamics.