KBEt²

Books and review papers covering Keldysh-Kadanoff-Baym equations

1. Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction,
   Gianluca Stefanucci and Robert van Leeuwen, Cambridge 2013
   
2. Nonequilibrium Green's Functions Approach to Inhomogeneous Systems,
   Karsten Balzer and Michael Bonitz, Springer Lecture Notes in Physics, vol. 867 (2013)
   
3. Progress in Nonequilibrium Greens Functions V,
   Robert van Leeuwen, Riku Tuovinen, and M. Bonitz (eds.), J. Phys. Conf. Ser. vol. 427 (2013)
   Comments: review papers on KBE. Contents and pdf-files of articles are freely available from this link to IoP
4. Progress in Nonequilibrium Greens Functions IV,
   M. Bonitz and K. Balzer (eds.), J. Phys. Conf. Ser. vol. 220 (2010)
   Comments: review papers on KBE. Contents and pdf-files of articles are freely available from this link to IoP
5. E. Calzetta, B. L. Hu,
   Nonequilibrium quantum field theory,
   Cambridge University Press, 2008
   Comment: overview of nonequilibrium statistical mechanics and QFT techniques including linear response theory, quantum kinetic theory and the hydrodynamical limit.
6. Introduction to Computational Methods for Many-Body Physics,
   M. Bonitz and D. Semkat (eds.), Rinton Press, Princeton 2006
   Comments: includes one extensive chapter on numerical solution of KBE for spatially homogeneous systems and discussion of initial correlations
7. Progress in Nonequilibrium Greens Functions III,
   M. Bonitz and A. Filinov (eds.), J. Phys. Conf. Ser. vol. 35 (2006)
   Comments: review papers on KBE. Online version is free
   discounted printed copies available, see contact
8. Progress in Nonequilibrium Greens Functions II,
   M. Bonitz and D. Semkat (eds.), World Scientific Publ., Singapore 2003
   Comments: review papers on KBE. Includes historical reviews by Leonid Keldysh and by Alex Abrikosov.
   discounted copies available, see contact
9. D. Kremp, M. Schlanges, W.-D. Kraeft,
   Quantum Statistics of Nonideal Plasmas, Springer (2005)
   Comments: includes details of two-time KBE, applications to transport and laser-matter interaction etc.
   
10. Progress in Nonequilibrium Greens Functions,
    M. Bonitz (ed.), World Scientific Publ., Singapore 2000
    Comments: review papers on KBE. Includes historical reviews by Paul C. Martin and by Gordon Baym.
11. M. Bonitz,
    Quantum Kinetic Theory, B.G. Teubner, Stuttgart, Leipzig, 1998
    Comments: extensive coverage of single-time quantum kientic equations (density operator formalism) and one chapter on relativistic and non-relativistic Keldysh-Kadanoff-Baym equations
12. H. Haug, A.P. Jauho,
    Quantum Kinetics in Transport and Optics of Semiconductors, Springer, 1996, Second, and substantially revised edition 2008
13. L.P. Kadanoff, G. Baym,
    Quantum Statistical Mechanics,
    Benjamin, New York, 1962
    further editions: Advanced book classics, Addison-Wesley, Reading 1989
    comments: THE standard text book reference on nonequilibrium Greens functions

Masters and PhD theses on Keldysh-Kadanoff-Baym equations

1. Sebastian Hermanns,
   Nonequilibrium Green's functions approach to Hubbard nano-clusters using the generalized Kadanoff-Baym ansatz,
   PhD thesis, Kiel University 2012, advisor: M. Bonitz
2. Karsten Balzer,
   Solving the Two-time Kadanoff-Baym Equations. Application to Model Atoms and Molecules,
   PhD thesis, Kiel University 2011, advisor: M. Bonitz
3. A. Hohenegger,
   Finite Density Aspects of Leptogenesis,
   PhD thesis, University Heidelberg 2009,
4. Lasse Rosenthal,
   Greens functions approach to electron-hole bilayers, (in German)
   Diploma thesis, Kiel University 2009, advisor: M. Bonitz
   pdf-file
   
5. Adrian Stan,
   Conserving approximations in nonequilibrium green function theory,
   PhD thesis, University Groningen 2009, advisor: R. van Leeuwen
   pdf-file
   
6. David Hochstuhl,
   Nonequilibrium Green functions approach to ionization processes,
   Diploma thesis, Kiel University 2008, advisor: M. Bonitz
   pdf-file
   
7. M. Garny,
   Particle Physics and Dark Energy: Beyond Classical Dynamics,
   PhD thesis, MPIK Heidelberg/TU Munich, 2008, advisor: M. Lindner
   pdf-file
   Comment: chapters 6-8 cover relativistic Kadanoff-Baym equations with initial correlations
8. Mahdi Pourfath,
   Numerical Study of Quantum Transport in Carbon Nanotube Based Transistors,
   PhD thesis, TU Wien 2007
9. Karsten Balzer,
   Nonequilibrium Green functions approach to artificial atoms,
   Diploma thesis, Kiel University 2007, advisor: M. Bonitz
   pdf-file
   
10. Andrea Fromm,
    Nonequilibrium Green functions approach to inhomogeneous semiconductors in strong electromagnetic fields, (in German)
    Diploma thesis, Kiel University 2006, advisor: M. Bonitz
    pdf-file
    
11. M. M. Müller,
    Comparison of Boltzmann Kinetics with Quantum Dynamics for Relativistic Quantum Fields,
    PhD thesis, TU Munich, 2006, advisor: M. Lindner
    pdf-file
    
12. Dirk Semkat,
    Initial correlations and memory effects in kinetic theory, (in German)
    Diploma thesis, Rostock University 1996
    advisors: D. Kremp and M. Bonitz

Papers

2011

1. T. Koch, A. Alvermann, H. Fehske
   Non-equilibrium transport through molecular junctions in the quantum regime
   arXiv:1105.0576v1
   
   
2. J. Marbach, F.X. Bronold, H. Fehske
   Auger de-excitation of metastable molecules at metallic surfaces
   arXiv:arXiv:1012.3576v2
   
   
3. A. Rios, B. Barker, M. Buchler, P. Danielewicz
   Towards a nonequilibrium Green’s function description of nuclear reactions: one-dimensional mean-field dynamics
   Ann. Phys. (N.Y.), 326, 1274-1319 (2011)
   doi: 10.1016/j.aop.2010.12.009
   arXiv:1009.0215v1
   
   

2010

1. M. Bonitz, D. Hochstuhl, S. Bauch, K. Balzer
   Quantum Kinetic Approach to Time-Resolved Photoionization of Atoms
   Contrib. Plasma Phys., 50, 54-59 (2010)
   doi: 10.1002/ctpp.201010012
   arXiv:0910.5458
   
   
2. K. Balzer, S. Bauch, M. Bonitz
   Efficient grid-based method in nonequilibrium Green's function calculations: Application to model atoms and molecules
   Phys. Rev. A, 81, 022510 (2010)
   doi: 10.1103/PhysRevA.81.022510
   Comment: first realization of two-time KBE approach to inhomogeneous systems in coordinate representation.
   
   
3. D. Hochstuhl, S. Bauch, M. Bonitz
   Multiconfigurational time-dependent Hartree-Fock calculations for photoionization of one-dimensional Helium
   J. Phys. Conf. Series, 220, 012019
   doi: 10.1088/1742-6596/220/1/012019
   arXiv:0911.0259
   
   
4. S. Bauch, D. Hochstuhl, K. Balzer, M. Bonitz
   Quantum breathing mode of interacting particles in harmonic traps
   J. Phys. Conf. Series, 220, 012013
   doi: 10.1088/1742-6596/220/1/012013
   
   
5. K. Balzer, S. Bauch, M. Bonitz
   Finite elements and the discrete variable representation in nonequilibrium Green's function
   J. Phys. Conf. Series, 220, 012020
   arXiv:0911.4348
   
   
6. D. Hochstuhl, K. Balzer, S. Bauch, M. Bonitz
   Nonequilibrium Green function approach to photoionization processes in atoms
   Proceedings of the international conference Frontiers of Quantum and Mesoscopic Thermodynamics FQMT '08
   Physica E, 42, 513-519 (2010)
   download pdf-file
   doi: 10.1016/j.physe.2009.06.044
   arXiv:0902.0768
   
   
7. K. Balzer, S. Bauch, M. Bonitz
   Time-dependent second-order Born calculations for model atoms and molecules in strong laser fields
   Phys. Rev. A, 82, 033427 (2010)
   doi: 10.1103/PhysRevA.82.033427
   arXiv:1008.4621
   Fig. 3c of this paper has been selected by Physical Review A for the Kaleidoscope
   
   
8. M. Puig von Friesen, C. Verdozzi, C.-O. Almbladh
   Kadanoff-Baym dynamics of Hubbard clusters: Performance of many-body schemes, correlation-induced damping and multiple steady and quasi-steady states
   Phys. Rev. B, 82, 155108 (2010)
   doi: 10.1103/PhysRevB.82.155108
   
   
9. P. Danielewicz, A. Rios, B. Barker
   Towards quantum transport for nuclear reactions
   Proceedings of the international conference Frontiers of Quantum and Mesoscopic Thermodynamics FQMT '08
   Physica E, 42, 501-507 (2010)
   doi: 10.1016/j.physe.2009.08.014
   
   
10. H. Minari, N. Mori
    A computationally cost-effective interleaving method for atomistic non-equilibrium Green's function simulation
    2008 International Workshop on Scientific Computing in Electronics Engineering (WSCEE 2008)
    Mathematical and Computer Modelling, 51, 888-892 (2010)
    doi: 10.1016/j.mcm.2009.08.035
    
    
11. A. Alvermann, H. Fehske
    Non-equilibrium current and electron pumping in nanostructures
    J. Phys. Conf. Series, 200, 012005 (2010)
    doi: 10.1088/1742-6596/200/1/012005
    
    

2009

1. M. Puig von Friesen, C. Verdozzi, and C.-O. Almbladh,
   Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters
   Phys. Rev. Lett. 103 (2009) 176404
   doi: 10.1103/PhysRevLett.103.176404
   
2. K. Balzer and M. Bonitz,
   Nonequilibrium properties of strongly correlated artificial atoms - a Green's functions approach
   J. Phys. A 42 (2009) 214020
   doi: 10.1088/1751-8113/42/21/214020
   arXiv:0810.2633
   download pdf-file
3. K. Balzer, M. Bonitz, R. van Leeuwen, N.E. Dahlen, and A. Stan,
   Nonequilibrium Green's functions approach to strongly correlated few-electron quantum dots
   Phys. Rev. B 79 (2009) 245306
   doi: 10.1103/PhysRevB.79.245306
   arXiv:0810.2425
   download pdf-file
   This paper has been selected for the June 2009 issue of Virtual Journal of Nanoscale Science & Technology,
   published by the American Physical Society and the American Institute of Physics.
4. S. Bauch, K. Balzer, C. Henning, and M. Bonitz,
   Quantum breathing mode of trapped bosons and fermions at arbitrary coupling
   Phys. Rev. B 80 (2009) 054515
   doi: 10.1103/PhysRevB.80.054515
   arXiv:0903.1993
   download pdf-file
   This paper has been selected for the September 2009 issue of Virtual Journal of Atomic Quantum Fluids,
   published by the American Physical Society and the American Institute of Physics.
   
5. M. Garny and M M Müller,
   Kadanoff-Baym equations with non-Gaussian initial conditions: The equilibrium limit
   Phys. Rev. D 80 (2009), 085011
   doi: 10.1103/PhysRevD.80.085011
   
6. W. Cassing,
   From Kadanoff-Baym dynamics to off-shell parton transport
   Eur. Phys. Journal - Special Topics 168 (2009), 3-87
   doi: 10.1140/epjst/e2009-00959-x
   
7. S. Borsanyi, U. Reinosa,
   Renormalised nonequilibrium quantum field theory: Scalar fields,
   doi: Phys.Rev.D80:125029,2009
   arXiv:0809.0496
   
8. A Stan, N E Dahlen, R van Leeuwen,
   Time propagation of the Kadanoff-Baym equations for inhomogeneous systems
   J. Chem. Phys. 130 (2009), 224101
   doi: 10.1063/1.3127247
   
9. A Stan, N E Dahlen, R van Leeuwen,
   Levels of self-consistency in the GW approximation
   J. Chem. Phys. 130 (2009), 114105
   doi: 10.1063/1.3089567
   
10. P. Myöhänen, A Stan, G. Stefanucci, and R van Leeuwen,
    Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime
    Phys. Rev. B 80 (2009), 115107
    doi: 10.1103/PhysRevB.80.115107
    
11. D.E. Petersen, S. Li, K. Stokbro, H.H.B. Sorensen, P.C. Hansen, S. Skelboe, and E. Darve,
    A hybrid method for the parallel computation of Green’s functions,
    Journal of Computational Physics 228, 5020-5039 (2009)
    doi: 10.1016/j.jcp.2009.03.035
    

2008

1. A. Yu. Zakharov,
   Variational Principle for Kadanoff-Baym Kinetic Equations
   Transport Theory and Statistical Physics 37, Issue 5-7 (2008) 613-623
   doi: 10.1080/00411450802515726
2. A. Hohenegger, A. Kartavtsev, M. Lindner,
   Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time
   Phys. Rev. D 78, (2008), 1-13
   doi: 10.1103/PhysRevD.78.085027
   arXiv:0807.4551v2
   
3. P. Myöhänen, A. Stan, G. Stefanucci and R. van Leeuwen,
   A many-body approach to quantum transport dynamics: Initial correlations and memory effects
   Europhys. Lett. 84, (2008) 67001
   doi: 10.1209/0295-5075/84/67001
   
4. M. Lindner, M. M. Müller,
   Comparison of Boltzmann kinetics with quantum dynamics for a chiral Yukawa model far from equilibrium,
   Phys. Rev. D 77, 2 (2008) 085027
   doi: 10.1103/PhysRevD.77.025027
   arXiv:0710.2917
   

2007

1. N E Dahlen, and R van Leeuwen,
   Solving the Kadanoff-Baym Equations for Inhomogeneous Systems: Application to Atoms and Molecules
   Phys. Rev. Lett. 98, 15 (2007) 153004
   doi: 10.1103/PhysRevLett.98.153004
   
2. M. Arshad, A. S. Kondratyev, and I. Siddique,
   Spectral function and kinetic equation for a normal Fermi liquid
   Phys. Rev. B 76, 5 (2007) 054306
   doi: 10.1103/PhysRevB.76.054306
   arXiv:cond-mat/0701292v2

2006

1. P Gartner, J Seebeck and F Jahnke,
   Relaxation properties of the quantum kinetics of carrier–LO-phonon interaction in quantum wells and quantum dots
   Phys. Rev. B 73 (2006) 115307
   doi: 10.1103/PhysRevB.73.115307
   arXiv:cond-mat/0510535v2
2. Nils Erik Dahlen, Robert van Leeuwen and Adrian Stan,
   Propagating the Kadanoff-Baym equations for atoms and molecules
   J. Phys. Conf. Ser. 35 (2006) 340
   doi: 10.1088/1742-6596/35/1/031
   
3. M M Müller,
   Comparing Boltzmann vs. Kadanoff-Baym
   J. Phys. Conf. Ser. 35 (2006) 390-397
   doi: 10.1088/1742-6596/35/1/036
   
4. M. Lindner, M. M. Müller,
   Comparison of Boltzmann equations with quantum dynamics for scalar fields,
   Phys. Rev D 73, 12 (2006) 125002
   doi: 10.1103/PhysRevD.73.125002
   arXiv:hep-ph/0512147
   

2005

1. NE Dahlen, and R van Leeuwen,
   Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation
   J. Chem. Phys. 122 (2005) 164102
   comments: first two-time solutions of the KBE for atoms
   doi: 10.1063/1.1884965
   
2. J. Berges,
   Introduction to nonequilibrium quantum field theory,
   AIP Conf.Proc. 739,1 (2005), 3-62
   doi: 10.1063/1.1843591
   arXiv:hep-ph/0409233
   

2003

1. DO Gericke, MS Murillo, D Semkat, M Bonitz, D Kremp,
   Relaxation of strongly coupled Coulomb systems after rapid changes of the interaction potential
   J. Phys. A 63 (2003)
   comments: cooling of many-body system after relaxation from overcorrelated initial state
   doi: 10.1088/0305-4470/36/22/334
2. D Semkat, M Bonitz, and D Kremp,
   Relaxation of a quantum many-body system from a correlated initial state. A general and consistent approach
   Contrib. Plasma Phys. 43, 5-6 (2003) 321-325
   doi: 10.1002/ctpp.200310037
   comments: general nonequilibrium initial state in single-time and two-time kinetic theory

2001

1. J. Knoll, Yu. B. Ivanov, and D. N. Voskresensky,
   Exact Conservation Laws of the Gradient Expanded Kadanoff–Baym Equations
   Ann. Phys. (N.Y.) 293 (2001) 126-146
   doi: 10.1006/aphy.2001.6185
   arXiv:nucl-th/0102044v1
   
2. HS Köhler and K Morawetz,
   Correlations in many-body systems with two-time Green’s functions
   Phys. Rev. C 64 (2001) 024613
   doi: 10.1103/PhysRevC.64.024613
   arXiv:nucl-th/0102059v2
   
3. K Morawetz, M Bonitz, V G Morozov, G Röpke, and D Kremp,
   Short-time dynamics with initial correlations
   Phys. Rev. E 62 (2001)
   doi: 10.1103/PhysRevE.63.020102
   

2000

1. N.H. Kwong, and M. Bonitz,
   Real-Time Kadanoff-Baym Approach to Plasma Oscillations in a Correlated Electron Gas
   Phys. Rev. Lett. 84 (2000) 1768-1771
   doi: 10.1103/PhysRevLett.84.1768
   comments: two-time solutions of the KBE for inhomogenous electron gas. computation of dynamical structure factor with vertex corrections from a nonequilibrium calculation.
2. D. Semkat, D. Kremp, and M. Bonitz,
   Kadanoff–Baym equations and non-Markovian Boltzmann equation in generalized T-matrix approximation
   J. Math. Phys. 41 (2000) 7458-7567
   doi: 10.1063/1.1286204
   comments: two-time solutions of the KBE in T-matrix approximation with initial correlations

1999

1. D. Semkat, D. Kremp, and M. Bonitz.
   Kadanoff-Baym equations with initial correlations
   Phys. Rev. E 59 (1999), 1557-1562
   doi: 10.1103/PhysRevE.59.1557
   comments: two-time solutions of the KBE for with nonequilibrium initial correlations. First demonstration of correlation (order) induced cooling
2. M. Bonitz, N. H. Kwong, D. Semkat, D. Kremp,
   Generalized Kadanoff-Baym Theory for Non-Equilibrium Many-Body Systems in External Fields. An Effective Multi-Band Approach
   Contrib. Plasma Phys. 39 (1999), 37-40
   doi: 10.1002/ctpp.2150390109
   comments: Keldysh-Kadanoff-Baym equations in an external field. Efficient subdivision of hamiltonian
3. N.H. Kwong, M. Bonitz, R. Binder and H.S. Köhler,
   Semiconductor Kadanoff-Baym Equation Results for Optically Excited Electron-Hole Plasmas in Quantum Wells
   phys. stat. sol. (b) 206 (1999), 197-203
   doi: 10.1002/(SICI)1521-3951(199803)206:1<197::AID-PSSB197>3.0.CO;2-9
   comments: two-time solution of KBE for semiconductor in stron laser field. Test of generalized Kadanoff-Baym ansatz
4. H.S. Köhler, N.H. Kwong, and H.A. Yousif,
   A Fortran code for solving the Kadanoff-Baym equations for a homogeneous fermion system
   Computer Physics Communications 123 issue 1-3 (1999), 123-142
   doi: 10.1016/S0010-4655(99)00260-X
   comments: the first publically available code for two-time solution of KBE
5. M. Bonitz, D. Semkat, H. Haug,
   Non-Lorentzian spectral functions for Coulomb quantum kinetics
   Eur. Phys. J. B 9 (1999), 309-314
   doi: 10.1007/s100510050770
   comments: test of GKBA with improved spectral function for case of Coulomb scattering, comparison with two-time solutions of KBE
6. P. Gartner, L. Banyai, and H. Haug,
   Two-time electron-LO-phonon quantum kinetics and the generalized Kadanoff-Baym approximation
   Phys. Rev. B 60 (1999), 14234-14241
   doi: 10.1103/PhysRevB.60.14234
   

1998

1. C. Greiner and S. Leupold,
   Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes
   Ann. Phys. (N.Y.) 270 (1995) 328-390
   doi: 10.1006/aphy.1998.5849
   

1997

1. P. Bozek,
   Particle production in quantum transport theories
   Phys. Rev. C 56 (1997) 1452-1456
   doi: 10.1103/PhysRevC.56.1452
   comments: two-time solutions of the KBE for nuclear collisions
2. R. Binder, H.S. Köhler, and M. Bonitz,
   Green's function description of momentum orientation relaxation of photo-excited electron plasmas in semiconductors
   Phys. Rev. B 55 (1997) 5110
   doi: 10.1103/PhysRevB.55.5110
   comments: two-time solutions of the KBE for Coulomb scattering in semiconductors, study of ultrafast isotropization of carrier distribution
3. M. Bonitz, D. Semkat and D. Kremp,
   Short-time Dynamics of Correlated Many-Particle Systems: Molecular Dynamics vs. Quantum Kinetics
   Phys. Rev. E 56 (1997) 1246
   doi: 10.1103/PhysRevE.56.1246
   comments: two-time solutions of the KBE for Coulomb scattering in plasmas, including effect of initial correlations, comparison with kinetic energy relaxation in classical molecular dynamics
4. M. Bonitz, R. Binder and H.S. Köhler,
   Quantum kinetic equations: Correlation dynamics and selfenergy
   Contrib. Plasma Phys. 37, 2-3 (1997) 101-113
   doi: 10.1002/ctpp.2150370202
   
5. H.S. Köhler and R. Binder,
   The Interplay of Electron-Phonon and Electron-Electron Scattering within the Two-Time Green's Function Description
   Contrib. Plasma Phys. 37 (1997) 167-172
   doi: 10.1002/ctpp.2150370208
   comments: first two-time solutions of the KBE for Coulomb scattering and electron-phonon scattering in semiconductors

1996

1. M. Bonitz, D. Kremp, D.C. Scott, R. Binder, W. D. Kraeft, H. S. Köhler,
   Numerical analysis of non-Markovian effects in charge-carrier scattering: one-time versus two-time kinetic equations
   J. Phys.: Cond. Matt. 8 (1996) 6057
   doi: 10.1088/0953-8984/8/33/012
   comments: first two-time solutions of the KBE including carrier-carrier scattering for semiconductors
2. W Schäfer,
   Influence of electron–electron scattering on femtosecond four-wave mixing in semiconductors
   JOSA B 13 (1996) 1291-1297
   doi: 10.1364/JOSAB.13.001291
   comments: two-time solutions of the KBE including carrier-carrier scattering for semiconductors
3. H Haug and L Banyai,
   Improved spectral functions for quantum kinetics
   Sol. State Comm. 100 (1996) 303-306
   doi: 10.1016/0038-1098(96)00504-2
   comments: Non-Lorentzian model for spectral function which is close to solution of two-time KBE for semiconductors with electron-phonon scattering

1995

1. H S Köhler,
   Memory and correlation effects in nuclear collisions
   Phys. Rev. C 51 (1995) 3232-3239
   doi: 10.1103/PhysRevC.51.3232
   comments: two-time solutions of the KBE for nuclear collisions

1992

1. M Hartmann and W Schäfer,
   Real Time Approach to Relaxation and Dephasing Processes in Semiconductors
   phys. stat. sol. (b) 173 (1992) 165-176
   doi: 10.1002/pssb.2221730117
   comments: first two-time solutions of the KBE in solid state physics including electron-phonon scattering.

1990

1. A.S. Kondrat'ev, I. E. Lyublinskaya and V. M. Uzdin,
   Spectral representation of nonequilibrium Green's functions in the Kadanoff-Baym technique
   Theoretical and Mathematical Physics 84 (1990) 773-776
   doi: 10.1007/BF01017203
   

1986

1. P Lipavsky, V Spicka and B Velicky,
   Generalized Kadanoff-Baym ansatz for deriving quantum transport equations
   Phys. Rev. B 34 (1986) 6933-6942
   doi: 10.1103/PhysRevB.34.6933
   comments: contains the derivation of the "GKBA" (Lipavsky ansatz) - reconstruction of the two-time correlation functions fromt the single-time density matrix in nonequilibrium and derives the corrections to the GKBA.

1984

1. P. Danielewicz,
   Quantum theory of nonequilibrium processes II. Application to nuclear collisions
   Ann. Phys. (N.Y.) 152 (1984) 305-326
   doi: 10.1016/0003-4916(84)90093-9
   comments: the first full two-time solution of the KBE (homogeneous nuclear matter). Includes treatment of a correlated initial state and comparison with Boltzmann kinetic theory.
2. P. Danielewicz,
   Quantum theory of nonequilibrium processes I.
   Ann. Phys. (N.Y.) 152 (1984) 239-304
   doi: 10.1016/0003-4916(84)90092-7
   

1965

1. L.V. Keldysh,
   Diagram Technique for Nonequilibrium Processes
   Soviet Phys. JETP 20 (1965) 1018
   original russian paper: Zh. Eksp. Teor. Fiz. 47, 1515 (1964)
   comments: the key paper on the extension of Feynman diagrams to arbitrary nonequilibrium systems by introducing the double time contour

1962

1. G. Baym,
   Self-consistent approximations in many-body systems
   Phys. Rev. 127 (1962) 1391
   doi: 10.1103/PhysRev.127.1391
   

1961

1. G. Baym, L.P. Kadanoff
   CONSERVATION LAWS AND CORRELATION FUNCTIONS
   Phys. Rev. 124 (1961) 287
   doi: 10.1103/PhysRev.124.287