A Brief History of the GKLS Equation

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

[1]  E. Størmer.  Positive linear maps of Cu * -algebras , 1974 .

[2]  E. Fermi.  Polarization of high energy protons scattered by nuclei , 1954 .

[3]  K. Kraus,et al.  Operations and measurements. II , 1970 .

[4]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[5]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[6]  C. Porter,et al.  Model for Nuclear Reactions with Neutrons , 1954 .

[7]  J. Neumann.  Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik , 1927 .

[8]  Hyunjoong Kim,et al.  Functional Analysis I , 2017 .

[9]  W. Stinespring.  Positive functions on *-algebras , 1955 .

[10]  E. Davies,et al.  Markovian master equations , 1974 .

[11]  Luigi Accardi,et al.  The Vacuum Distributions of the Truncated Virasoro Fields are Products of Gamma Distributions , 2017, Open Syst. Inf. Dyn..

[12]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[13]  K. Kraus,et al.  States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin , 1983 .

[14]  Man-Duen Choi.  Completely positive linear maps on complex matrices , 1975 .

[15]  Marshall Baker,et al.  Lectures on quantum mechanics , 2014, Quantum Information Processing.

[16]  F. Haake.  Statistical treatment of open systems by generalized master equations , 1973 .

[17]  Rudolf Haag,et al.  Local observables and particle statistics II , 1971 .

[18]  M. Sentís.  Quantum theory of open systems , 2002 .

[19]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[20]  P. M. Mathews,et al.  STOCHASTIC DYNAMICS OF QUANTUM-MECHANICAL SYSTEMS , 1961 .

[21]  R. Zwanzig.  Ensemble Method in the Theory of Irreversibility , 1960 .

[22]  W. Lamb.  Theory of an optical maser , 1964 .

[23]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[24]  OPEN QUANTUM DYNAMICS: COMPLETE POSITIVITY AND ENTANGLEMENT , 2005, quant-ph/0507271.

[25]  A remark on the expectations of operator algebras , 1960 .

[26]  R. Kubo.  Statistical Physics II: Nonequilibrium Statistical Mechanics , 2003 .

[27]  Günther Ludwig,et al.  Attempt of an axiomatic foundation of quantum mechanics and more general theories, II , 1967 .

[28]  W. Arveson.  On subalgebras of $C^*$-algebras , 1969 .

[29]  K. Kraus,et al.  Pure operations and measurements , 1969 .

[30]  E. Davies,et al.  Quantum stochastic processes , 1969 .

[31]  L. Hove,et al.  Quantum-mechanical perturbations giving rise to a statistical transport equation , 1954 .

[32]  Bernhard H. Haak,et al.  Open Quantum Systems , 2019, Tutorials, Schools, and Workshops in the Mathematical Sciences.

[33]  G. Agarwal.  I Master Equation Methods in Quantum Optics , 1973 .

[34]  L. Landau.  Das Dämpfungsproblem in der Wellenmechanik , 1927 .

[35]  A. Jamiołkowski.  Linear transformations which preserve trace and positive semidefiniteness of operators , 1972 .

[36]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[37]  E. Størmer.  Positive linear maps of operator algebras , 2012 .

[38]  S. Nakajima,et al.  On Quantum Theory of Transport Phenomena , 1959 .

[39]  A. Kossakowski,et al.  On quantum statistical mechanics of non-Hamiltonian systems , 1972 .

[40]  S. Woronowicz.  Positive maps of low dimensional matrix algebras , 1976 .

[41]  G.,et al.  On the Theory of Relaxation Processes * , 2022 .

[42]  W. Weidlich,et al.  Coherence-properties of the statistical operator in a laser model , 1965 .

[43]  Noam Chomsky,et al.  The Chomsky Reader , 1987 .

[44]  John E. Roberts,et al.  Local observables and particle statistics I , 1971 .

[45]  Gniewomir Sarbicki,et al.  Entanglement witnesses: construction, analysis and classification , 2014, 1402.2413.

[46]  S. Nakajima.  On Quantum Theory of Transport Phenomena Steady Diffusion , 1958 .

[47]  R. Xu,et al.  Theory of open quantum systems , 2002 .

[48]  D. Yevick,et al.  Laser theory , 1984, IEEE Journal of Quantum Electronics.

[49]  William Arveson,et al.  Subalgebras ofC*-algebras , 1969 .

[50]  G. Lindblad.  Completely positive maps and entropy inequalities , 1975 .

[51]  E. Davies,et al.  The harmonic oscillator in a heat bath , 1973 .

[52]  D. Walls.  Quantum Statistics of Nonlinear Optics , 1986 .

[53]  K. Kraus.  General state changes in quantum theory , 1971 .

[54]  J. Pillis.  Linear transformations which preserve hermitian and positive semidefinite operators. , 1967 .

[55]  E. Davies,et al.  Quantum stochastic processes II , 1970 .

[56]  Luigi Accardi,et al.  The First 40 Years of GKSL Generators and Some Proposal for the Future , 2017, Open Syst. Inf. Dyn..

[57]  H. Haken,et al.  Quantummechanical solutions of the laser masterequation. II , 1967 .

[58]  Liang Jiang,et al.  Geometry and Response of Lindbladians , 2015 .

[59]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[60]  Man-Duen Choi,et al.  Positive Linear Maps on C*-Algebras , 1972, Canadian Journal of Mathematics.

[61]  Kristian Kirsch,et al.  Methods Of Modern Mathematical Physics , 2016 .

[62]  R. Ingarden,et al.  On the connection of nonequilibrium information thermodynamics with non-hamiltonian quantum mechanics of open systems , 1975 .

[63]  V. Paulsen.  Completely Bounded Maps and Operator Algebras: Completely Bounded Multilinear Maps and the Haagerup Tensor Norm , 2003 .

[64]  Günter Dähn,et al.  Attempt of an axiomatic foundation of quantum mechanics and more general theories. IV , 1968 .