Abstract
In this book section, we give a brief introduction to many-body perturbation theory for coupled fermion-boson systems using non-equilibrium Green’s functions . Using the language of modern many-body perturbation theory and the so-called contour-ordered correlators, a single consistent formalism arises which can be applied to a multitude of classes of systems.
This is a preview of subscription content, log in via an institution.
References
Almbladh CO, von Barth U, van Leeuwen R (1999) Variational total energies from Φ- and Ψ- derivable theories. Int J Mod Phys B 13(05n06):535–541. http://www.worldscientific.com/doi/abs/10.1142/S0217979299000436
Arrachea L, Mucciolo ER, Chamon C, Capaz RB (2012) Microscopic model of a phononic refrigerator. Phys Rev B 86(12):125424. https://link.aps.org/doi/10.1103/PhysRevB.86.125424, arXiv:1203.2561v2
Baym G (1962) Self-consistent approximations in many-body systems. Phys Rev 127(4):1391–1401. http://prola.aps.org/abstract/PR/v127/i4/p1391_1; https://link.aps.org/doi/10.1103/PhysRev.127.1391
Baym G, Kadanoff LP (1961) Conservation laws and correlation functions. Phys Rev 124(2):287–299. http://prola.aps.org/abstract/PR/v124/i2/p287_1; https://link.aps.org/doi/10.1103/PhysRev.124.287
Bloch I, Zwerger W (2008) Many-body physics with ultracold gases. Rev Mod Phys 80(3): 885–964. http://link.aps.org/doi/10.1103/RevModPhys.80.885
Bonitz M (2016) Quantum kinetic theory. Springer International Publishing, Cham. http://link.springer.com/10.1007/978-3-319-24121-0
Boström EV, Mikkelsen A, Verdozzi C, Perfetto E, Stefanucci G (2018) Charge separation in donor–C 60 complexes with real-time green functions: the importance of nonlocal correlations. Nano Lett 18(2):785–792. http://pubs.acs.org/doi/10.1021/acs.nanolett.7b03995
Bruus H, Flensberg K (2004) Introduction to many-body quantum theory in condensed matter physics. Oxford University Press, Oxford
Cuevas JC, Scheer E (2010) Molecular electronics. World Scientific Publishing, Singapore
Dahlen N, van Leeuwen R (2007) Solving the Kadanoff-Baym equations for inhomogeneous systems: application to atoms and molecules. Phys Rev Lett 98(15):153004. http://link.aps.org/doi/10.1103/PhysRevLett.98.153004
Datta S (2005) Quantum transport: atom to transistor. https://doi.org/10.1017/CBO9781139164313; http://books.google.com/books?hl=en&lr=&id=Yj50EJoS224C&oi=fnd&pg=PR9&dq=Quantum+Transport+:+Atom+to+Transistor&ots=jmVfovCmEu&sig=oYLWTfZuNxd44-WwK4FwD-Tmg98
De Dominicis C (1963) Variational statistical mechanics in terms of “Observables” for normal and superfluid systems. J Math Phys 4(2):255–265. http://aip.scitation.org/doi/10.1063/1.1703949
Fetter AL, Walecka JD (2003) Quantum theory of many-particle theory. Dover Publications, New York
Flick J, Ruggenthaler M, Appel H, Rubio A (2017) Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry. Proc Natl Acad Sci 114(12):3026–3034. http://www.pnas.org/lookup/doi/10.1073/pnas.1615509114
Hedin L (1965) New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys Rev 139(3A). http://link.aps.org/doi/10.1103/PhysRev.139.A796
Hedin L, Lundqvist S (1970) Effects of electron-electron and electron-phonon interactions on the one-electron states of solids. Solid State Phys Adv Res Appl 23:1–181. https://doi.org/10.1016/S0081-1947(08)60615-3; http://linkinghub.elsevier.com/retrieve/pii/S0081194708606153
Henneberger K, Moldzio U, Güldner H (2000) Correlation effects and quantum kinetics in pulse excited semiconductors. In: Progress in Nonequilibrium Green’s Functions. World Scientific, pp 180–211. https://doi.org/10.1142/9789812793812_0015; http://www.worldscientific.com/doi/abs/10.1142/9789812793812_0015
Karlsson D, van Leeuwen R (2016) Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule. Phys Rev B 94(12):125124. https://link.aps.org/doi/10.1103/PhysRevB.94.125124
Khosravi E, Uimonen AM, Stan A, Stefanucci G, Kurth S, van Leeuwen R, Gross E (2012) Correlation effects in bistability at the nanoscale: steady state and beyond. Phys Rev B 85(7):075103. http://link.aps.org/doi/10.1103/PhysRevB.85.075103
Latini S, Perfetto E, Uimonen AM, van Leeuwen R, Stefanucci G (2014) Charge dynamics in molecular junctions: nonequilibrium Green’s function approach made fast. Phys Rev B 89(7):075306. http://link.aps.org/doi/10.1103/PhysRevB.89.075306
Lipavský P, Špička V, Velický B (1986) Generalized Kadanoff-Baym ansatz for deriving quantum transport equations. Phys Rev B 34(10):6933–6942. http://prb.aps.org/abstract/PRB/v34/i10/p6933_1
Mahfouzi F, Nikolić BK (2014) Signatures of electron-magnon interaction in charge and spin currents through magnetic tunnel junctions: a nonequilibrium many-body perturbation theory approach. Phys Rev B 90(4):045115. https://link.aps.org/doi/10.1103/PhysRevB.90.045115; 1310.8551
Martin PC, Schwinger J (1959) Theory of many-particle systems. I. Phys Rev 115(6):1342–1373. https://link.aps.org/doi/10.1103/PhysRev.115.1342
de Melo PMMC, Marini A (2016) Unified theory of quantized electrons, phonons, and photons out of equilibrium: A simplified ab initio approach based on the generalized Baym-Kadanoff ansatz. Phys Rev B 93(15):155102. https://link.aps.org/doi/10.1103/PhysRevB.93.155102
Myöhänen P, Stan A, Stefanucci G, van Leeuwen R (2008) A many-body approach to quantum transport dynamics: initial correlations and memory effects. EPL Europhysics Lett 84(6):67001. https://doi.org/10.1209/0295-5075/84/67001; http://stacks.iop.org/0295-5075/84/i=6/a=67001?key=crossref.7f76c45bb53d32a8d0f63a9c53ac212b
Myöhänen P, Stan A, Stefanucci G, van Leeuwen R (2009) Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime. Phys Rev B 80(11):115,107, https://doi.org/10.1103/PhysRevB.80.115107, URL http://prb.aps.org/abstract/PRB/v80/i11/e115107 https://link.aps.org/doi/10.1103/PhysRevB.80.115107
Myöhänen P, Tuovinen R, Korhonen T, Stefanucci G, van Leeuwen R (2012) Image charge dynamics in time-dependent quantum transport. Phys Rev B 85(7):075105. http://prb.aps.org/abstract/PRB/v85/i7/e075105; https://link.aps.org/doi/10.1103/PhysRevB.85.075105
Perfetto E, Uimonen AM, van Leeuwen R, Stefanucci G (2015) First-principles nonequilibrium Green’s-function approach to transient photoabsorption: application to atoms. Phys Rev A 92(3):033419. http://link.aps.org/doi/10.1103/PhysRevA.92.033419
Perfetto E, Sangalli D, Marini A, Stefanucci G (2018) Ultrafast charge migration in XUV photoexcited phenylalanine: a first-principles study based on real-time nonequilibrium Green’s functions. J Phys Chem Lett 9(6):1353–1358. http://pubs.acs.org/doi/10.1021/acs.jpclett.8b00025
Puig von Friesen M, Verdozzi C, Almbladh CO (2010) 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(15):155108. http://link.aps.org/doi/10.1103/PhysRevB.82.155108
Ruggenthaler M, Flick J, Pellegrini C, Appel H, Tokatly IV, Rubio A (2014) Quantum-electrodynamical density-functional theory: bridging quantum optics and electronic-structure theory. Phys Rev A At Mol Opt Phys 90(1):1–26. https://doi.org/10.1103/PhysRevA.90.012508, 1403.5541
Säkkinen N (2016) Application of time-dependent many-body perturbation theory to excitation spectra of selected finite model systems. PhD thesis, University of Jyväskylä. http://urn.fi/URN:ISBN:978-951-39-6814-4
Säkkinen N, Peng Y, Appel H, van Leeuwen R (2015a) Many-body Green’s function theory for electron-phonon interactions: ground state properties of the Holstein dimer. J Chem Phys 143(23):234101. https://doi.org/10.1063/1.4936142; http://aip.scitation.org/doi/10.1063/1.4936142, 1403.2968
Säkkinen N, Peng Y, Appel H, van Leeuwen R (2015b) Many-body Green’s function theory for electron-phonon interactions: the Kadanoff-Baym approach to spectral properties of the Holstein dimer. J Chem Phys 143(23):234102. https://doi.org/10.1063/1.4936143 http://aip.scitation.org/doi/10.1063/1.4936143, 1507.04726
Schlünzen N, Hermanns S, Bonitz M, Verdozzi C (2016) Dynamics of strongly correlated fermions: Ab initio results for two and three dimensions. Phys Rev B 93(3):035107. https://link.aps.org/doi/10.1103/PhysRevB.93.035107
Schüler M, Berakdar J, Pavlyukh Y (2016) Time-dependent many-body treatment of electron-boson dynamics: application to plasmon-accompanied photoemission. Phys Rev B 93(5):054303. https://link.aps.org/doi/10.1103/PhysRevB.93.054303, 1510.08650
Sentef MA, Kemper AF, Georges A, Kollath C (2016) Theory of light-enhanced phonon-mediated superconductivity. Phys Rev B 93(14):144506. https://link.aps.org/doi/10.1103/PhysRevB.93.144506, 1505.07575
Špička V, Velický B, Kalvová A (2014) Electron systems out of equilibrium: nonequilibrium Green’s function approach. Int J Mod Phys B 28(23):1430013. https://doi.org/10.1142/S0217979214300138; http://www.worldscientific.com/doi/abs/10.1142/S0217979214300138?journalCode=ijmpb&quickLinkVolume=28&quickLinkIssue=23&quickLinkPage=1430013&selectedTab=citation&volume=28#.VvAQ0PsV1sE.mendeley
Stan A, Dahlen NE, van Leeuwen R (2009) Time propagation of the Kadanoff-Baym equations for inhomogeneous systems. J Chem Phys 130(22):224101. https://doi.org/10.1063/1.3127247; http://www.ncbi.nlm.nih.gov/pubmed/19530756
Stefanucci G, Almbladh CO (2004) Time-dependent partition-free approach in resonant tunneling systems. Phys Rev B 69(19):195318. https://link.aps.org/doi/10.1103/PhysRevB.69.195318
Stefanucci G, van Leeuwen R (2013) Nonequilibrium many-body theory of quantum systems: a modern introduction. Cambridge University Press, Cambridge
Tuovinen R, Säkkinen N, Karlsson D, Stefanucci G, van Leeuwen R (2016) Phononic heat transport in the transient regime: an analytic solution. Phys Rev B 93(21):214301. http://arxiv.org/abs/1604.02298; http://link.aps.org/doi/10.1103/PhysRevB.93.214301
Uimonen AM, Khosravi E, Stefanucci G, Kurth S, van Leeuwen R, Gross EKU (2010) Real-time switching between multiple steady-states in quantum transport. J Phys Conf Ser 220(1):012018. https://doi.org/10.1088/1742-6596/220/1/012018; http://stacks.iop.org/1742-6596/220/i=1/a=012018
Uimonen AM, Khosravi E, Stan A, Stefanucci G, Kurth S, van Leeuwen R, Gross EKU (2011) Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model. Phys Rev B 84(11):115103. http://prb.aps.org/abstract/PRB/v84/i11/e115103; https://link.aps.org/doi/10.1103/PhysRevB.84.115103
Wang JS, Agarwalla BK, Li H, Thingna J (2014) Nonequilibrium Green’s function method for quantum thermal transport. Front Phys 9(6):673–697. http://link.springer.com/10.1007/s11467-013-0340-x, 1303.7317
Wick GC (1950) The evaluation of the collision matrix. Phys Rev 80(2):268–272. https://link.aps.org/doi/10.1103/PhysRev.80.268
Acknowledgements
Several of the derivations in this work were based on the PhD thesis of Niko Säkkinen. D.K. acknowledges the Academy of Finland for funding under Project No. 308697.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
Karlsson, D., Leeuwen, R.v. (2018). Non-equilibrium Green’s Functions for Coupled Fermion-Boson Systems. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_8-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-42913-7_8-1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42913-7
Online ISBN: 978-3-319-42913-7
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics