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The local Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) quantum master equation is a powerful tool for the study of open quantum many-body systems.
The dynamical theory of nuclear induction
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On the theory of relaxation processes
A. G. Redfield · 1957
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On Quantum Theory of Transport Phenomena: Steady Diffusion
Sadao Nakajima · 1958
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Ensemble method in the theory of irreversibility
Robert Zwanzig · 1960
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Relaxation phenomena in spin and harmonic oscillator systems
Jayaseetha Rau · 1963
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The theory of relaxation processes
A.G. Redfield · 1965
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The finite group velocity of quantum spin systems
E.H. Lieb and D.W. Robinson · 1972
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Markovian master equations
E. B. Davies · 1974
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Completely positive dynamical semigroups of n‐level systems
Vittorio Gorini, Andrzej Kossakowski, and E. C. G. Sudarshan · 1976
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On the generators of quantum dynamical semigroups
G. Lindblad · 1976
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Fluctuations in radiative processes
Claude Cohen-Tannoudji · 1986
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From completely positive maps to the quantum Markovian semigroup master equation
Daniel A. Lidar, Zsolt Bihary, and K.Birgitta Whaley · 2001
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The theory of open quantum systems
Heinz-Peter Breuer, Francesco Petruccione, et al · 2002
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Five Lectures on Dissipative Master Equations
Berthold-Georg Englert and Giovanna Morigi · 2002
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Measuring irreversible dynamics of a quantum harmonic oscillator
Giovanna Morigi, Enrique Solano, Berthold-Georg Englert, and Herbert Walther · 2002
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Thermalizing quantum machines: Dissipation and entanglement
Valerio Scarani, Mário Ziman, Peter Štelmachovič, Nicolas Gisin, and Vladimír Bužek · 2002
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Fourier’s law confirmed for a class of small quantum systems
Mathias Michel, Michael Hartmann, Jochen Gemmer, and Guenter Mahler · 2003
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Heat transport in quantum spin chains
Carlos Mejia-Monasterio and Hannu Wichterich · 2007
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Modeling heat transport through completely positive maps
Hannu Wichterich, Markus J. Henrich, Heinz-Peter Breuer, Jochen Gemmer, and Mathias Michel · 2007
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Preservation of positivity by dynamical coarse graining
Gernot Schaller and Tobias Brandes · 2008
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Third quantization: a general method to solve master equations for quadratic open fermi systems
Tomaž Prosen · 2008
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Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
Giuliano Benenti, Giulio Casati, Toma ž Prosen, Davide Rossini, and Marko Žnidarič · 2009
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Equivalence of transport coefficients in bath-induced and dynamical scenarios
R. Steinigeweg, M. Ogiewa, and J. Gemmer · 2009
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Quantum nonequilibrium steady states induced by repeated interactions
Dragi Karevski and Thierry Platini · 2009
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Systematic perturbation theory for dynamical coarse-graining
Gernot Schaller, Philipp Zedler, and Tobias Brandes · 2009
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Lieb-robinson bound and locality for general markovian quantum dynamics
David Poulin · 2010
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Quantization over boson operator spaces
Tomaž Prosen and Thomas H Seligman · 2010
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Exact solution of markovian master equations for quadratic fermi systems: thermal baths, open xy spin chains and non-equilibrium phase transition
Tomaž Prosen and Bojan Žunkovič · 2010
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An open-system quantum simulator with trapped ions
Julio T Barreiro, Markus Müller, Philipp Schindler, Daniel Nigg, Thomas Monz, Michael Chwalla, Markus Hennrich, Christian F Roos, Peter Zoller, and Rainer Blatt · 2011
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Open XXZ spin chain: Nonequilibrium steady state and a strict bound on ballistic transport
Tomaž Prosen · 2011
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Exact nonequilibrium steady state of a strongly driven open x x z xxz chain
Phenomenological position and energy resolving Lindblad approach to quantum kinetics
Gediminas Kiršanskas, Martin Franckié, and Andreas Wacker · 2018
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Open-quantum-system dynamics: Recovering positivity of the Redfield equation via the partial secular approximation
Donato Farina and Vittorio Giovannetti · 2019
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Anomalous decay of coherence in a dissipative many-body system
Raphaël Bouganne, Manel Bosch Aguilera, Alexis Ghermaoui, Jérôme Beugnon, and Fabrice Gerbier · 2020
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Thermalization in open many-body systems based on eigenstate thermalization hypothesis
Tatsuhiko Shirai and Takashi Mori · 2020
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Completely positive master equation for arbitrary driving and small level spacing
Evgeny Mozgunov and Daniel Lidar · 2020
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Toma ž Prosen · 2011
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Engineered open systems and quantum simulations with atoms and ions
Markus Müller, Sebastian Diehl, Guido Pupillo, and Peter Zoller · 2012
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Quantum transport efficiency and Fourier’s law
Daniel Manzano, Markus Tiersch, Ali Asadian, and Hans J. Briegel · 2012
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Controlling the dynamics of an open many-body quantum system with localized dissipation
G. Barontini, R. Labouvie, F. Stubenrauch, A. Vogler, V. Guarrera, and H. Ott · 2013
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Coarse graining can beat the rotating-wave approximation in quantum Markovian master equations
Christian Majenz, Tameem Albash, Heinz-Peter Breuer, and Daniel A. Lidar · 2013
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Quantum trajectories and open many-body quantum systems
Andrew J. Daley · 2014
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The local approach to quantum transport may violate the second law of thermodynamics
Amikam Levy and Ronnie Kosloff · 2014
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Frederik Nathan and Mark S. Rudner · 2020
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Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
Dragomir Davidović · 2020
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Perturbation theory for Lindblad superoperators for interacting open quantum systems
V. Yu. Shishkov, E. S. Andrianov, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky · 2020
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Accuracy assessment of perturbative master equations: Embracing nonpositivity
Richard Hartmann and Walter T. Strunz · 2020
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Emerging dissipative phases in a superradiant quantum gas with tunable decay
Francesco Ferri, Rodrigo Rosa-Medina, Fabian Finger, Nishant Dogra, Matteo Soriente, Oded Zilberberg, Tobias Donner, and Tilman Esslinger · 2021
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Finite-temperature transport in one-dimensional quantum lattice models
B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, and M. Žnidarič · 2021
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Irreversible entropy production: From classical to quantum
Gabriel T. Landi and Mauro Paternostro · 2021
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Local master equations bypass the secular approximation
Stefano Scali, Janet Anders, and Luis A. Correa · 2021
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Lindbladian approximation beyond ultraweak coupling
Tobias Becker, Ling-Na Wu, and André Eckardt · 2021
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Nonequilibrium boundary-driven quantum systems: Models, methods, and properties
Gabriel T. Landi, Dario Poletti, and Gernot Schaller · 2022
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Environment-induced decay dynamics of antiferromagnetic order in mott-hubbard systems
G. Schaller, F. Queisser, N. Szpak, J. König, and R. Schützhold · 2022
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Fundamental limitations in lindblad descriptions of systems weakly coupled to baths
Devashish Tupkary, Abhishek Dhar, Manas Kulkarni, and Archak Purkayastha · 2022
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Local master equations may fail to describe dissipative critical behavior
Michael Konopik and Eric Lutz · 2022
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Quantum collision models: Open system dynamics from repeated interactions
Francesco Ciccarello, Salvatore Lorenzo, Vittorio Giovannetti, and G. Massimo Palma · 2022
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High accuracy steady states obtained from the Universal Lindblad Equation, 2022
Frederik Nathan and Mark S. Rudner · 2022
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Searching for lindbladians obeying local conservation laws and showing thermalization
Devashish Tupkary, Abhishek Dhar, Manas Kulkarni, and Archak Purkayastha · 2023
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Global becomes local: Efficient many-body dynamics for global master equations, 2023
Alexander Schnell · 2023
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Floquet states in open quantum systems
Takashi Mori · 2023
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Fate of entanglement in magnetism under lindbladian or non-markovian dynamics and conditions for their transition to landau-lifshitz-gilbert classical dynamics
Federico Garcia-Gaitan and Branislav K. Nikolić · 2024
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