Nonequilibrium many-body theory of quantum systems : a modern introduction /
Stefanucci, Gianluca, 1973-
Nonequilibrium many-body theory of quantum systems : a modern introduction / Gianluca Stefanucci, University of Rome Tor Vergata, Italy, Robert van Leeuwen, University of Jyväskylä, Finland. - Cambridge : Cambridge University Press, 2013. - 1 online resource (xvii, 600 pages) : illustrations
Includes bibliographical references and index.
""Contents""; ""Preface""; ""List of abbreviations and acronyms""; ""Fundamental constants and basic relations""; ""1 Second quantization""; ""1.1 Quantum mechanics of one particle""; ""1.2 Quantum mechanics of many particles""; ""1.3 Quantum mechanics of many identical particles""; ""1.4 Field operators""; ""1.5 General basis states""; ""1.6 Hamiltonian in second quantization""; ""1.7 Density matrices and quantum averages""; ""2 Getting familiar with second quantization: model Hamiltonians""; ""2.1 Model Hamiltonians""; ""2.2 Pariser�Parr�Pople model""; ""2.3 Noninteracting models"" ""2.3.1 Bloch theorem and band structure""""2.3.2 Fano model""; ""2.4 Hubbard model""; ""2.4.1 Particle�hole symmetry: application to the Hubbard dimer""; ""2.5 Heisenberg model""; ""2.6 BCS model and the exact Richardson solution""; ""2.7 Holstein model""; ""2.7.1 Peierls instability""; ""2.7.2 Lang�Firsov transformation: the heavy polaron""; ""3 Time-dependent problems and equations of motion""; ""3.1 Introduction""; ""3.2 Evolution operator""; ""3.3 Equations of motion for operators in the Heisenberg picture""; ""3.4 Continuity equation: paramagnetic and diamagnetic currents"" ""3.5 Lorentz Force""""4 The contour idea""; ""4.1 Time-dependent quantum averages""; ""4.2 Time-dependent ensemble averages""; ""4.3 Initial equilibrium and adiabatic switching""; ""4.4 Equations of motion on the contour""; ""4.5 Operator correlators on the contour""; ""5 Many-particle Green�s functions""; ""5.1 Martin�Schwinger hierarchy""; ""5.2 Truncation of the hierarchy""; ""5.3 Exact solution of the hierarchy from Wick�s theorem""; ""5.4 Finite and zero-temperature formalism from the exact solution""; ""5.5 Langreth rules""; ""6 One-particle Green�s function"" ""6.1 What can we learn from G?""""6.1.1 The inevitable emergence of memory""; ""6.1.2 Matsubara Green�s function and initial preparations""; ""6.1.3 Lesser/greater Green�s function: relaxation and quasi-particles""; ""6.2 Noninteracting Green�s function""; ""6.2.1 Matsubara component""; ""6.2.2 Lesser and greater components""; ""6.2.3 All other components and a useful exercise""; ""6.3 Interacting Green�s function and Lehmann representation""; ""6.3.1 Steady-states, persistent oscillations,initial-state dependence"" ""6.3.2 Fluctuation�dissipation theorem and otherexact properties""""6.3.3 Spectral function and probability interpretation""; ""6.3.4 Photoemission experiments and interaction effects""; ""6.4 Total energy from the Galitskii�Migdal formula""; ""7 Mean field approximations""; ""7.1 Introduction""; ""7.2 Hartree approximation""; ""7.2.1 Hartree equations""; ""7.2.2 Electron gas""; ""7.2.3 Quantum discharge of a capacitor""; ""7.3 Hartree�Fock approximation""; ""7.3.1 Hartree�Fock equations""; ""7.3.2 Coulombic electron gas and spin-polarized solutions""
"The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics"--
English.
9781107341203 (electronic bk.) 1107341205 (electronic bk.) 1139023977 (electronic bk.) 9781139023979 (electronic bk.) 9781299749429 (MyiLibrary) 1299749429 (MyiLibrary) 9781107344952 1107344956 9781107347458 1107347459 1107348641 9781107348646 1107343704 9781107343702
CL0500000299 Safari Books Online
Green's functions.
Many-body problem.
Quantum theory--Mathematics.
Fonctions de Green.
Problème des N corps.
Théorie quantique--Mathématiques.
SCIENCE--Physics.
SCIENCE--Physics--Mathematical & Computational.
Green's functions.
Many-body problem.
Quantum theory--Mathematics.
Kwantummechanica.
Veel-deeltjes-systemen.
Electronic books.
QC174.17.G68 / S74 2013eb
530.1/5353
Nonequilibrium many-body theory of quantum systems : a modern introduction / Gianluca Stefanucci, University of Rome Tor Vergata, Italy, Robert van Leeuwen, University of Jyväskylä, Finland. - Cambridge : Cambridge University Press, 2013. - 1 online resource (xvii, 600 pages) : illustrations
Includes bibliographical references and index.
""Contents""; ""Preface""; ""List of abbreviations and acronyms""; ""Fundamental constants and basic relations""; ""1 Second quantization""; ""1.1 Quantum mechanics of one particle""; ""1.2 Quantum mechanics of many particles""; ""1.3 Quantum mechanics of many identical particles""; ""1.4 Field operators""; ""1.5 General basis states""; ""1.6 Hamiltonian in second quantization""; ""1.7 Density matrices and quantum averages""; ""2 Getting familiar with second quantization: model Hamiltonians""; ""2.1 Model Hamiltonians""; ""2.2 Pariser�Parr�Pople model""; ""2.3 Noninteracting models"" ""2.3.1 Bloch theorem and band structure""""2.3.2 Fano model""; ""2.4 Hubbard model""; ""2.4.1 Particle�hole symmetry: application to the Hubbard dimer""; ""2.5 Heisenberg model""; ""2.6 BCS model and the exact Richardson solution""; ""2.7 Holstein model""; ""2.7.1 Peierls instability""; ""2.7.2 Lang�Firsov transformation: the heavy polaron""; ""3 Time-dependent problems and equations of motion""; ""3.1 Introduction""; ""3.2 Evolution operator""; ""3.3 Equations of motion for operators in the Heisenberg picture""; ""3.4 Continuity equation: paramagnetic and diamagnetic currents"" ""3.5 Lorentz Force""""4 The contour idea""; ""4.1 Time-dependent quantum averages""; ""4.2 Time-dependent ensemble averages""; ""4.3 Initial equilibrium and adiabatic switching""; ""4.4 Equations of motion on the contour""; ""4.5 Operator correlators on the contour""; ""5 Many-particle Green�s functions""; ""5.1 Martin�Schwinger hierarchy""; ""5.2 Truncation of the hierarchy""; ""5.3 Exact solution of the hierarchy from Wick�s theorem""; ""5.4 Finite and zero-temperature formalism from the exact solution""; ""5.5 Langreth rules""; ""6 One-particle Green�s function"" ""6.1 What can we learn from G?""""6.1.1 The inevitable emergence of memory""; ""6.1.2 Matsubara Green�s function and initial preparations""; ""6.1.3 Lesser/greater Green�s function: relaxation and quasi-particles""; ""6.2 Noninteracting Green�s function""; ""6.2.1 Matsubara component""; ""6.2.2 Lesser and greater components""; ""6.2.3 All other components and a useful exercise""; ""6.3 Interacting Green�s function and Lehmann representation""; ""6.3.1 Steady-states, persistent oscillations,initial-state dependence"" ""6.3.2 Fluctuation�dissipation theorem and otherexact properties""""6.3.3 Spectral function and probability interpretation""; ""6.3.4 Photoemission experiments and interaction effects""; ""6.4 Total energy from the Galitskii�Migdal formula""; ""7 Mean field approximations""; ""7.1 Introduction""; ""7.2 Hartree approximation""; ""7.2.1 Hartree equations""; ""7.2.2 Electron gas""; ""7.2.3 Quantum discharge of a capacitor""; ""7.3 Hartree�Fock approximation""; ""7.3.1 Hartree�Fock equations""; ""7.3.2 Coulombic electron gas and spin-polarized solutions""
"The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics"--
English.
9781107341203 (electronic bk.) 1107341205 (electronic bk.) 1139023977 (electronic bk.) 9781139023979 (electronic bk.) 9781299749429 (MyiLibrary) 1299749429 (MyiLibrary) 9781107344952 1107344956 9781107347458 1107347459 1107348641 9781107348646 1107343704 9781107343702
CL0500000299 Safari Books Online
Green's functions.
Many-body problem.
Quantum theory--Mathematics.
Fonctions de Green.
Problème des N corps.
Théorie quantique--Mathématiques.
SCIENCE--Physics.
SCIENCE--Physics--Mathematical & Computational.
Green's functions.
Many-body problem.
Quantum theory--Mathematics.
Kwantummechanica.
Veel-deeltjes-systemen.
Electronic books.
QC174.17.G68 / S74 2013eb
530.1/5353