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Classical and celestial mechanics : the Recife lectures / edited by Hildeberto Cabral and Florin Diacu
Classical and celestial mechanics : the Recife lectures / edited by Hildeberto Cabral and Florin Diacu
Pubbl/distr/stampa Princeton, NJ : Princeton University Press, c2002
Descrizione fisica xviii, 385 p. : ill. ; 24 cm
Disciplina 521
Altri autori (Persone) Cabral, Hildeberto
Diacu, Florin
Soggetto topico Many-body problem
Celestial mechanics
Mechanics
ISBN 0691050228
Classificazione AMS 70F15
LC QB362.M3C52
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Central configurations and relative equilibria for the N-Body problem / Dieter Schmidt ; App. A. The Area of a Triangle ; App. B. Mathematica Code for the Four-Body Problem ; App. C. Mathematica Code for the Planar Five-Body Problem. Singularities of the N-Body Problem / Florin Diacu. Lectures on the Two-Body Problem / Alain Albony. Normal Forms of Hamiltonian Systems and Stability of Equilibria / Hildeberto Eulalio Cabral. Poincare's Compactification and Applications to Celestial Mechanics / Ernesto Perez-Chavela. The Motion of the Moon / Dieter Schmidt ; App. A. Canonical Transformation to Jacobi Coordinates ; App. B. MACSYMA Program for the Intermediate Orbit ; App. C. MACSYMA Program for Inclination ; App. D. MACSYMA Program for First Order Terms in e Lectures on Geometrical Methods in Mechanics / Mark Levi. Momentum Maps and Geometric Phases / Jair Koiller. Bifurcation from Families of Periodic Solutions / Jack K. Hale and Placido Taboas
Record Nr. UNISALENTO-991000945249707536
Princeton, NJ : Princeton University Press, c2002
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui
Classical many-body problems amenable to exact treatments : solvable and/or integrable and/or linearizable... in one-, two-, and three- dimensional space / Francesco Calogero
Classical many-body problems amenable to exact treatments : solvable and/or integrable and/or linearizable... in one-, two-, and three- dimensional space / Francesco Calogero
Autore Calogero, F.
Pubbl/distr/stampa Berlin ; New York : Springer, c2001
Descrizione fisica xviii, 749 p. ; 24 cm.
Disciplina 521
Collana Lecture notes in physics. New series m, Monographs ; m66
Lecture notes in physics. Monographs, 0940-7677 ; m66
Soggetto topico Many-body problem
ISBN 3540417648 (alk. paper)
Classificazione LC QB362.M3
53.1.64
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991004039029707536
Calogero, F.  
Berlin ; New York : Springer, c2001
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui
Collapse of metastability : dynamics of first-order phase transition / / Seiji Miyashita
Collapse of metastability : dynamics of first-order phase transition / / Seiji Miyashita
Autore Miyashita Seiji
Pubbl/distr/stampa Singapore : , : Springer, , [2022]
Descrizione fisica 1 online resource (260 pages)
Disciplina 016.61483
Collana Fundamental Theories of Physics
Soggetto topico Quantum theory
Many-body problem
ISBN 9789811966682
9789811966675
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Concept of Metastability -- 1.1.1 Life Time of a Metastable State -- Part I Metastability in Classical Systems -- 2 Metastability in Thermodynamic Systems -- 2.1 Introduction -- 2.2 Mean-Field Theory for a Ferromagnetic Ising System -- 2.2.1 Self-consistent Equation of the Magnetization -- 2.2.2 Magnetization Curve -- 2.2.3 Free Energy as a Function of Magnetization -- 2.3 Rotation of Magnetization -- 2.3.1 Stoner-Wohlfarth Model -- 2.3.2 Stoner-Wohlfarth Diagram -- 2.3.3 Trajectrory -- 2.4 First-Order Phase Transitions as a Function of the Temperature -- 2.4.1 A Model with Many Degeneracy of Zero Energy States -- 2.4.2 Blume-Capel Model -- 2.4.3 Spin Crossover Systems -- 2.5 Landau Theory -- 2.5.1 Landau Theory for Temperature Induced First-Order Phase Transition -- 2.6 Gas-Liquid Phase Transition -- 2.6.1 Phenomenological Method: van der Waals (vDW) Equation -- 2.7 Statistical Treatments of the Gas-Liquid Phase Transition -- 2.7.1 Perturbational Approach -- 2.7.2 Lattice-Gas Model Approach -- 2.7.3 Mean-Field Analysis for the Lattice Gas Model -- 3 Escape Rate from the Metastable State -- 3.1 Introduction -- 3.2 Arrhenius Law -- 3.3 Kramers Method -- 3.4 Spinodal Singularity -- 3.4.1 Master Equation for the Husimi-Temperley Model -- 3.5 Nucleation in Model Short-Range Interaction -- 3.6 Dynamical Spinodal Point -- 3.7 Survival Probability of a Metastable State -- 3.7.1 Néel-Arrhenius Process -- 4 Spatial Pattern During the Transition -- 4.1 Dynamics Associated with the First-Order Phase Transition -- 4.2 Dynamics After the Temperature Quenching -- 4.2.1 Non-conserved System: k squared tk2t Scaling -- 4.2.2 A Stretched Exponential Law for Spin-Autocorrelation Function -- 4.2.3 Conserved System: Lifshitz-Slyozov-Wigner Theory k cubed tk3t Scaling -- 4.2.4 Ostwald Ripening.
Part II First-Order Phase Transition from Viewpoints of the Eigenvalue Problem -- 5 Structure of Eigenvalues for the First-Order Phase Transition -- 5.1 Transfer Matrix -- 5.1.1 Ladder Systems -- 5.1.2 Free Energy -- 5.1.3 Correlation Functions -- 5.1.4 Temperature Dependence of the Eigenvalues -- 5.1.5 Field Dependence of the Eigenvalues Below the Critical Temperature -- 5.2 Eigenvalue Analysis of Dynamical Processes -- 5.2.1 Eigenstates of Master Equation -- 5.2.2 Approach to the Stationary State -- 5.3 Kinetic Ising Model -- 5.3.1 Demonstration in a Small System of 2 times 22times2 System -- 5.3.2 Master Equation for the Magnetization for a Model with Long-Range Interaction -- 5.3.3 Relaxation times of 4 times 34times3 System -- 5.4 Eigenvalue Problem of Quantum Master Equation -- 5.5 Free Energy at the First-Order Phase Transition -- 5.6 Langer's Argument -- 5.6.1 Langer's Analysis I: A Picture of Nucleation Cluster -- 5.6.2 Langer's Analysis II: Functional Integral -- 5.6.3 Langer's Analysis III: A Picture of the Action -- 5.6.4 Langer's Estimation of Decay Rate of Metastable State -- Part III Metastability in Quantum Systems -- 6 Collapse of Metastability by the Quantum Fluctuation -- 6.1 Introduction -- 6.2 Quantum Mechanical States in Double-Well Type Potential -- 6.2.1 Chracteristics of Metastability in the Eigenstate Spectrum StartSet upper E Subscript i Baseline left parenthesis h right parenthesis EndSet{Ei(h)} as a Function of Field -- 6.3 Characterstic of Eigenvalue Structure Around the First-Order Phase Transition -- 6.4 Particle Conveyance by a Potential-Well -- 6.4.1 Sudden Start by Changing the Velocity from Zero to cc -- 6.4.2 Smooth Acceleration -- 6.4.3 Scattering Problem -- 6.4.4 Relaxation from Metastable Potential -- 6.4.5 Carry Up the Particle -- 6.5 Quantum Tunneling in Magnetic Systems.
6.5.1 Metastability in Magnetic Systems -- 6.6 Relaxation of Magnetism in Small Systems -- 6.7 Single Molecular Magnets (SMM) -- 6.7.1 Tunneling Under Dissipation -- 6.7.2 Dynamics in Dissipative Environments -- 6.8 Magnetic Foehn Effect -- 6.9 Effect of Dissipation on the Relaxation of Metastable State -- 6.9.1 Free-Boson Bath Model -- 6.9.2 Dynamics of the Magnetization in Uniaxial Anisoropy -- 6.9.3 Effects of Dissipation on the Hybridized Lowest Two States -- 6.10 Quantum Stoner-Wohlfarth Model -- 6.10.1 Dynamics of Magnetization -- 6.10.2 Distribution of the Population over the States -- 6.10.3 Dynamics of Magnetization in Dissipative Environment -- 6.11 Nucleation in Quantum Systems -- 6.12 Transverse-Ising Model -- 6.12.1 Visualization of Quantum and Classical Fluctuation in a left parenthesis d plus 1 right parenthesis(d+1) Dimensional Representation of States -- 6.13 Cooperative Phenomena in a Cavity System -- 6.13.1 Cavity System -- 6.13.2 Phase Transitions of the Dicke Hamiltonian -- 6.14 Optical Bistability -- 6.14.1 Mean-Field Analysis -- 6.14.2 Analogy to a Picture of Thermodynamic Free Energy -- 6.14.3 Numerical Study of the Size Dependence -- 6.14.4 Metastability in the Bistable Region -- 6.14.5 Hysteresis Phenomena -- 6.15 Limit Cycle of the Hysteresis -- 6.15.1 Dynamics Under an Driving Force with Periodically Oscillating Amplitude -- 6.15.2 Floquet Map -- 6.15.3 Mean-Field Analysis of Limit Cycle -- Part IV Quantitative Estimation of Relaxation Time -- 7 Coercivity of Magnets -- 7.1 Introduction -- 7.2 Coercivity Estimated by the Free Energy Landscape -- 7.2.1 Minimum Energy Path (MEP) Method -- 7.2.2 Free Energy Landscape Method -- 7.3 Characteristic Quantities of Magnetization Reversal -- 7.3.1 Activation Volume -- 7.3.2 Magnetic Viscosity.
7.3.3 Relation Between the Activation Volume upper V Subscript normal aVa and the Magnetic Viscosity upper SS -- 7.3.4 Coercivity Obtained by a Direct Simulation of SLLG -- 7.3.5 Coercivity of Large Grains -- 7.4 Coercivity of Magnets as an Ensemble of Grains -- Part V Appendices -- 8 Appendices -- 8.1 Brief Review on the Mean-Field Approximation -- 8.1.1 Basic Idea of Mean-Field Theory -- 8.1.2 Mean-Field Free Energy as a Function of the Magnetization F(m:T,H) -- 8.1.3 Free Energy in Bragg-Williams Approximation -- 8.1.4 Free Energy of the Long-Range Interaction Model (Husimi-Temperley Model) -- 8.1.5 Free Energy as a Variational Function -- 8.2 Equation of Stochastic Processes -- 8.2.1 Master Equation and Fokker-Planck Equation -- 8.2.2 Master Equation in Differential Form -- 8.2.3 Symmetrization of the Time-Evolution Operator -- 8.2.4 Master Equation for Continuous Variable -- 8.2.5 Brownian Motion -- 8.3 Landau-Zener Scattering -- 8.4 Quantum Master Equation -- 8.4.1 Lindblad Type -- 8.4.2 Redfield Type -- 8.4.3 Redfield Type for a Single Spin -- 8.4.4 Bloch Equation -- 8.4.5 Under a Time-Dependent Field -- 8.5 Path-Integral Method -- 8.5.1 One Particle Problem -- 8.5.2 Partition Function at a Finite Temperature -- 8.5.3 Onsager-Machlup Formula for Stochastic Process -- 8.6 WKB Approximation -- 8.6.1 Semiclassical Approximation -- 8.6.2 Connection Formula -- 8.6.3 Bound State -- 8.6.4 Transmission Coefficient by WKB Approximation -- 8.6.5 Transition Matrix -- 8.6.6 Relaxation from Metastable Potential -- Appendix References -- -- Index.
Record Nr. UNINA-9910629293903321
Miyashita Seiji  
Singapore : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Collapse of metastability : dynamics of first-order phase transition / / Seiji Miyashita
Collapse of metastability : dynamics of first-order phase transition / / Seiji Miyashita
Autore Miyashita Seiji
Pubbl/distr/stampa Singapore : , : Springer, , [2022]
Descrizione fisica 1 online resource (260 pages)
Disciplina 016.61483
Collana Fundamental Theories of Physics
Soggetto topico Quantum theory
Many-body problem
ISBN 9789811966682
9789811966675
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Concept of Metastability -- 1.1.1 Life Time of a Metastable State -- Part I Metastability in Classical Systems -- 2 Metastability in Thermodynamic Systems -- 2.1 Introduction -- 2.2 Mean-Field Theory for a Ferromagnetic Ising System -- 2.2.1 Self-consistent Equation of the Magnetization -- 2.2.2 Magnetization Curve -- 2.2.3 Free Energy as a Function of Magnetization -- 2.3 Rotation of Magnetization -- 2.3.1 Stoner-Wohlfarth Model -- 2.3.2 Stoner-Wohlfarth Diagram -- 2.3.3 Trajectrory -- 2.4 First-Order Phase Transitions as a Function of the Temperature -- 2.4.1 A Model with Many Degeneracy of Zero Energy States -- 2.4.2 Blume-Capel Model -- 2.4.3 Spin Crossover Systems -- 2.5 Landau Theory -- 2.5.1 Landau Theory for Temperature Induced First-Order Phase Transition -- 2.6 Gas-Liquid Phase Transition -- 2.6.1 Phenomenological Method: van der Waals (vDW) Equation -- 2.7 Statistical Treatments of the Gas-Liquid Phase Transition -- 2.7.1 Perturbational Approach -- 2.7.2 Lattice-Gas Model Approach -- 2.7.3 Mean-Field Analysis for the Lattice Gas Model -- 3 Escape Rate from the Metastable State -- 3.1 Introduction -- 3.2 Arrhenius Law -- 3.3 Kramers Method -- 3.4 Spinodal Singularity -- 3.4.1 Master Equation for the Husimi-Temperley Model -- 3.5 Nucleation in Model Short-Range Interaction -- 3.6 Dynamical Spinodal Point -- 3.7 Survival Probability of a Metastable State -- 3.7.1 Néel-Arrhenius Process -- 4 Spatial Pattern During the Transition -- 4.1 Dynamics Associated with the First-Order Phase Transition -- 4.2 Dynamics After the Temperature Quenching -- 4.2.1 Non-conserved System: k squared tk2t Scaling -- 4.2.2 A Stretched Exponential Law for Spin-Autocorrelation Function -- 4.2.3 Conserved System: Lifshitz-Slyozov-Wigner Theory k cubed tk3t Scaling -- 4.2.4 Ostwald Ripening.
Part II First-Order Phase Transition from Viewpoints of the Eigenvalue Problem -- 5 Structure of Eigenvalues for the First-Order Phase Transition -- 5.1 Transfer Matrix -- 5.1.1 Ladder Systems -- 5.1.2 Free Energy -- 5.1.3 Correlation Functions -- 5.1.4 Temperature Dependence of the Eigenvalues -- 5.1.5 Field Dependence of the Eigenvalues Below the Critical Temperature -- 5.2 Eigenvalue Analysis of Dynamical Processes -- 5.2.1 Eigenstates of Master Equation -- 5.2.2 Approach to the Stationary State -- 5.3 Kinetic Ising Model -- 5.3.1 Demonstration in a Small System of 2 times 22times2 System -- 5.3.2 Master Equation for the Magnetization for a Model with Long-Range Interaction -- 5.3.3 Relaxation times of 4 times 34times3 System -- 5.4 Eigenvalue Problem of Quantum Master Equation -- 5.5 Free Energy at the First-Order Phase Transition -- 5.6 Langer's Argument -- 5.6.1 Langer's Analysis I: A Picture of Nucleation Cluster -- 5.6.2 Langer's Analysis II: Functional Integral -- 5.6.3 Langer's Analysis III: A Picture of the Action -- 5.6.4 Langer's Estimation of Decay Rate of Metastable State -- Part III Metastability in Quantum Systems -- 6 Collapse of Metastability by the Quantum Fluctuation -- 6.1 Introduction -- 6.2 Quantum Mechanical States in Double-Well Type Potential -- 6.2.1 Chracteristics of Metastability in the Eigenstate Spectrum StartSet upper E Subscript i Baseline left parenthesis h right parenthesis EndSet{Ei(h)} as a Function of Field -- 6.3 Characterstic of Eigenvalue Structure Around the First-Order Phase Transition -- 6.4 Particle Conveyance by a Potential-Well -- 6.4.1 Sudden Start by Changing the Velocity from Zero to cc -- 6.4.2 Smooth Acceleration -- 6.4.3 Scattering Problem -- 6.4.4 Relaxation from Metastable Potential -- 6.4.5 Carry Up the Particle -- 6.5 Quantum Tunneling in Magnetic Systems.
6.5.1 Metastability in Magnetic Systems -- 6.6 Relaxation of Magnetism in Small Systems -- 6.7 Single Molecular Magnets (SMM) -- 6.7.1 Tunneling Under Dissipation -- 6.7.2 Dynamics in Dissipative Environments -- 6.8 Magnetic Foehn Effect -- 6.9 Effect of Dissipation on the Relaxation of Metastable State -- 6.9.1 Free-Boson Bath Model -- 6.9.2 Dynamics of the Magnetization in Uniaxial Anisoropy -- 6.9.3 Effects of Dissipation on the Hybridized Lowest Two States -- 6.10 Quantum Stoner-Wohlfarth Model -- 6.10.1 Dynamics of Magnetization -- 6.10.2 Distribution of the Population over the States -- 6.10.3 Dynamics of Magnetization in Dissipative Environment -- 6.11 Nucleation in Quantum Systems -- 6.12 Transverse-Ising Model -- 6.12.1 Visualization of Quantum and Classical Fluctuation in a left parenthesis d plus 1 right parenthesis(d+1) Dimensional Representation of States -- 6.13 Cooperative Phenomena in a Cavity System -- 6.13.1 Cavity System -- 6.13.2 Phase Transitions of the Dicke Hamiltonian -- 6.14 Optical Bistability -- 6.14.1 Mean-Field Analysis -- 6.14.2 Analogy to a Picture of Thermodynamic Free Energy -- 6.14.3 Numerical Study of the Size Dependence -- 6.14.4 Metastability in the Bistable Region -- 6.14.5 Hysteresis Phenomena -- 6.15 Limit Cycle of the Hysteresis -- 6.15.1 Dynamics Under an Driving Force with Periodically Oscillating Amplitude -- 6.15.2 Floquet Map -- 6.15.3 Mean-Field Analysis of Limit Cycle -- Part IV Quantitative Estimation of Relaxation Time -- 7 Coercivity of Magnets -- 7.1 Introduction -- 7.2 Coercivity Estimated by the Free Energy Landscape -- 7.2.1 Minimum Energy Path (MEP) Method -- 7.2.2 Free Energy Landscape Method -- 7.3 Characteristic Quantities of Magnetization Reversal -- 7.3.1 Activation Volume -- 7.3.2 Magnetic Viscosity.
7.3.3 Relation Between the Activation Volume upper V Subscript normal aVa and the Magnetic Viscosity upper SS -- 7.3.4 Coercivity Obtained by a Direct Simulation of SLLG -- 7.3.5 Coercivity of Large Grains -- 7.4 Coercivity of Magnets as an Ensemble of Grains -- Part V Appendices -- 8 Appendices -- 8.1 Brief Review on the Mean-Field Approximation -- 8.1.1 Basic Idea of Mean-Field Theory -- 8.1.2 Mean-Field Free Energy as a Function of the Magnetization F(m:T,H) -- 8.1.3 Free Energy in Bragg-Williams Approximation -- 8.1.4 Free Energy of the Long-Range Interaction Model (Husimi-Temperley Model) -- 8.1.5 Free Energy as a Variational Function -- 8.2 Equation of Stochastic Processes -- 8.2.1 Master Equation and Fokker-Planck Equation -- 8.2.2 Master Equation in Differential Form -- 8.2.3 Symmetrization of the Time-Evolution Operator -- 8.2.4 Master Equation for Continuous Variable -- 8.2.5 Brownian Motion -- 8.3 Landau-Zener Scattering -- 8.4 Quantum Master Equation -- 8.4.1 Lindblad Type -- 8.4.2 Redfield Type -- 8.4.3 Redfield Type for a Single Spin -- 8.4.4 Bloch Equation -- 8.4.5 Under a Time-Dependent Field -- 8.5 Path-Integral Method -- 8.5.1 One Particle Problem -- 8.5.2 Partition Function at a Finite Temperature -- 8.5.3 Onsager-Machlup Formula for Stochastic Process -- 8.6 WKB Approximation -- 8.6.1 Semiclassical Approximation -- 8.6.2 Connection Formula -- 8.6.3 Bound State -- 8.6.4 Transmission Coefficient by WKB Approximation -- 8.6.5 Transition Matrix -- 8.6.6 Relaxation from Metastable Potential -- Appendix References -- -- Index.
Record Nr. UNISA-996499864403316
Miyashita Seiji  
Singapore : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
A course in quantum many-body theory : from conventional Fermi liquids to strongly correlated systems / / Michele Fabrizio
A course in quantum many-body theory : from conventional Fermi liquids to strongly correlated systems / / Michele Fabrizio
Autore Fabrizio Michele
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (350 pages)
Disciplina 530.144
Collana Graduate texts in physics
Soggetto topico Many-body problem
Quantum theory
ISBN 9783031163050
9783031163043
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Second Quantization -- 1.1 Fock States and Space -- 1.2 Fermionic Operators -- 1.2.1 Fermi Fields -- 1.2.2 Second Quantisation of Multiparticle Operators -- 1.3 Bosonic Operators -- 1.3.1 Bose Fields and Multiparticle Operators -- 1.4 Canonical Transformations -- 1.4.1 Canonical Transformations with Charge Non-conserving Hamiltonians -- 1.4.2 Harmonic Oscillators -- 1.5 Application: Electrons in a Box -- 1.6 Application: Electron Lattice Models and Emergence of Magnetism -- 1.6.1 Hubbard Models -- 1.6.2 Mott Insulators and Heisenberg Models -- 1.7 Application: Spin-Wave Theory -- 1.7.1 Classical Ground State -- 1.8 Beyond the Classical Limit: The Spin-Wave Approximation -- 1.8.1 Hamiltonian of Quantum Fluctuations -- 1.8.2 Spin-Wave Dispersion and Goldstone Theorem -- 1.8.3 Validity of the Approximation and the Mermin-Wagner Theorem -- 1.8.4 Order from Disorder -- Problems -- 2 Linear Response Theory -- 2.1 Linear Response Functions -- 2.2 Kramers-Kronig Relations -- 2.2.1 Symmetries -- 2.3 Fluctuation-Dissipation Theorem -- 2.4 Spectral Representation -- 2.5 Power Dissipation -- 2.5.1 Absorption/Emission Processes -- 2.5.2 Thermodynamic Susceptibilities -- 2.6 Application: Linear Response to an Electromagnetic Field -- 2.6.1 Quantisation of the Electromagnetic Field -- 2.6.2 System's Sources for the Electromagnetic Field -- 2.6.3 Optical Constants -- 2.6.4 Linear Response in the Longitudinal Case -- 2.6.5 Linear Response in the Transverse Case -- 2.6.6 Power Dissipated by the Electromagnetic Field -- Problems -- 3 Hartree-Fock Approximation -- 3.1 Hartree-Fock Approximation for Fermions at Zero Temperature -- 3.1.1 Alternative Approach -- 3.2 Hartree-Fock Approximation for Fermions at Finite Temperature -- 3.2.1 Saddle Point Solution -- 3.3 Time-Dependent Hartree-Fock Approximation.
3.3.1 Bosonization of the Low-Energy Particle-Hole Excitations -- 3.4 Application: Antiferromagnetism in the Half-Filled Hubbard Model -- 3.4.1 Spin-Wave Spectrum by Time-Dependent Hartree-Fock -- Problems -- 4 Feynman Diagram Technique -- 4.1 Preliminaries -- 4.1.1 Imaginary-Time Ordered Products -- 4.1.2 Matsubara Frequencies -- 4.1.3 Single-Particle Green's Functions -- 4.2 Perturbation Expansion in Imaginary Time -- 4.2.1 Wick's Theorem -- 4.3 Perturbation Theory for the Single-Particle Green's Function … -- 4.3.1 Diagram Technique in Momentum and Frequency Space -- 4.3.2 The Dyson Equation -- 4.3.3 Skeleton Diagrams -- 4.3.4 Physical Meaning of the Self-energy -- 4.3.5 Emergence of Quasiparticles -- 4.4 Other Kinds of Perturbations -- 4.4.1 Scalar Potential -- 4.4.2 Coupling to Bosonic Modes -- 4.5 Two-Particle Green's Functions and Correlation Functions -- 4.5.1 Diagrammatic Representation of the Two-Particle Green's Function -- 4.5.2 Correlation Functions -- 4.6 Coulomb Interaction and Proper and Improper Response Functions -- 4.7 Irreducible Vertices and the Bethe-Salpeter Equations -- 4.7.1 Particle-Hole Channel -- 4.7.2 Particle-Particle Channel -- 4.7.3 Self-energy and Irreducible Vertices -- 4.8 The Luttinger-Ward Functional -- 4.8.1 Thermodynamic Potential -- 4.9 Ward-Takahashi Identities -- 4.9.1 Ward-Takahashi Identity for the Heat Density -- 4.10 Conserving Approximation Schemes -- 4.10.1 Conserving Hartree-Fock Approximation -- 4.10.2 Conserving GW Approximation -- 4.11 Luttinger's Theorem -- 4.11.1 Validity Conditions for Luttinger's Theorem -- 4.11.2 Luttinger's Theorem in Presence of Quasiparticles and in Periodic Systems -- Problems -- 5 Landau's Fermi Liquid Theory -- 5.1 Emergence of Quasiparticles Reexamined -- 5.2 Manipulating the Bethe-Salpeter Equation -- 5.2.1 A Lengthy but Necessary Preliminary Calculation.
5.2.2 Interaction Vertex and Density-Vertices -- 5.3 Linear Response Functions -- 5.3.1 Response Functions of Densities Associated to Conserved Quantities -- 5.4 Thermodynamic Susceptibilities -- 5.4.1 Charge Compressibility -- 5.4.2 Spin Susceptibility -- 5.4.3 Specific Heat -- 5.5 Current-Current Response Functions -- 5.5.1 Thermal Response -- 5.5.2 Coulomb Interaction -- 5.6 Mott Insulators with a Luttinger Surface -- 5.7 Luttinger's Theorem and Quasiparticle Distribution Function -- 5.7.1 Oshikawa's Topological Derivation of Luttinger's Theorem -- 5.8 Quasiparticle Hamiltonian and Landau-Boltzmann Transport Equation -- 5.8.1 Landau-Boltzmann Transport Equation for Quasiparticles -- 5.8.2 Transport Equation in Presence of an Electromagnetic Field -- 5.9 Application: Transport Coefficients with Rotational Symmetry -- 6 Brief Introduction to Luttinger Liquids -- 6.1 What Is Special in One Dimension? -- 6.2 Interacting Spinless Fermions -- 6.2.1 Bosonized Expression of the Non-interacting Hamiltonian -- 6.2.2 Bosonic Representation of the Fermi Fields -- 6.2.3 Operator Product Expansion -- 6.2.4 Non-interacting Green's Functions and Density-Density Response Functions -- 6.2.5 Interaction -- 6.2.6 Interacting Green's Functions and Correlation Functions -- 6.2.7 Umklapp Scattering -- 6.2.8 Behaviour Close to the K=1/2 Marginal Case -- 6.3 Spin-1/2 Heisenberg Chain -- 6.4 The One-Dimensional Hubbard Model -- 6.4.1 Luttinger Versus Fermi Liquids -- Problems -- 7 Kondo Effect and the Physics of the Anderson Impurity Model -- 7.1 Brief Introduction to Scattering Theory -- 7.1.1 General Analysis of the Phase-Shifts -- 7.2 The Anderson Impurity Model -- 7.2.1 Non Interacting Impurity -- 7.2.2 Hartree-Fock Approximation -- 7.3 From the Anderson Impurity Model to the Kondo Model -- 7.3.1 The Emergence of Logarithmic Singularities and the Kondo Temperature.
7.3.2 Anderson's Poor Man's Scaling -- 7.4 Noziéres's Local Fermi Liquid Theory -- 7.4.1 Ward-Takahashi Identity -- 7.4.2 Luttinger's Theorem and Thermodynamic Susceptibilities -- Problems.
Record Nr. UNINA-9910629298003321
Fabrizio Michele  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
A course in quantum many-body theory : from conventional Fermi liquids to strongly correlated systems / / Michele Fabrizio
A course in quantum many-body theory : from conventional Fermi liquids to strongly correlated systems / / Michele Fabrizio
Autore Fabrizio Michele
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (350 pages)
Disciplina 530.144
Collana Graduate texts in physics
Soggetto topico Many-body problem
Quantum theory
ISBN 9783031163050
9783031163043
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Second Quantization -- 1.1 Fock States and Space -- 1.2 Fermionic Operators -- 1.2.1 Fermi Fields -- 1.2.2 Second Quantisation of Multiparticle Operators -- 1.3 Bosonic Operators -- 1.3.1 Bose Fields and Multiparticle Operators -- 1.4 Canonical Transformations -- 1.4.1 Canonical Transformations with Charge Non-conserving Hamiltonians -- 1.4.2 Harmonic Oscillators -- 1.5 Application: Electrons in a Box -- 1.6 Application: Electron Lattice Models and Emergence of Magnetism -- 1.6.1 Hubbard Models -- 1.6.2 Mott Insulators and Heisenberg Models -- 1.7 Application: Spin-Wave Theory -- 1.7.1 Classical Ground State -- 1.8 Beyond the Classical Limit: The Spin-Wave Approximation -- 1.8.1 Hamiltonian of Quantum Fluctuations -- 1.8.2 Spin-Wave Dispersion and Goldstone Theorem -- 1.8.3 Validity of the Approximation and the Mermin-Wagner Theorem -- 1.8.4 Order from Disorder -- Problems -- 2 Linear Response Theory -- 2.1 Linear Response Functions -- 2.2 Kramers-Kronig Relations -- 2.2.1 Symmetries -- 2.3 Fluctuation-Dissipation Theorem -- 2.4 Spectral Representation -- 2.5 Power Dissipation -- 2.5.1 Absorption/Emission Processes -- 2.5.2 Thermodynamic Susceptibilities -- 2.6 Application: Linear Response to an Electromagnetic Field -- 2.6.1 Quantisation of the Electromagnetic Field -- 2.6.2 System's Sources for the Electromagnetic Field -- 2.6.3 Optical Constants -- 2.6.4 Linear Response in the Longitudinal Case -- 2.6.5 Linear Response in the Transverse Case -- 2.6.6 Power Dissipated by the Electromagnetic Field -- Problems -- 3 Hartree-Fock Approximation -- 3.1 Hartree-Fock Approximation for Fermions at Zero Temperature -- 3.1.1 Alternative Approach -- 3.2 Hartree-Fock Approximation for Fermions at Finite Temperature -- 3.2.1 Saddle Point Solution -- 3.3 Time-Dependent Hartree-Fock Approximation.
3.3.1 Bosonization of the Low-Energy Particle-Hole Excitations -- 3.4 Application: Antiferromagnetism in the Half-Filled Hubbard Model -- 3.4.1 Spin-Wave Spectrum by Time-Dependent Hartree-Fock -- Problems -- 4 Feynman Diagram Technique -- 4.1 Preliminaries -- 4.1.1 Imaginary-Time Ordered Products -- 4.1.2 Matsubara Frequencies -- 4.1.3 Single-Particle Green's Functions -- 4.2 Perturbation Expansion in Imaginary Time -- 4.2.1 Wick's Theorem -- 4.3 Perturbation Theory for the Single-Particle Green's Function … -- 4.3.1 Diagram Technique in Momentum and Frequency Space -- 4.3.2 The Dyson Equation -- 4.3.3 Skeleton Diagrams -- 4.3.4 Physical Meaning of the Self-energy -- 4.3.5 Emergence of Quasiparticles -- 4.4 Other Kinds of Perturbations -- 4.4.1 Scalar Potential -- 4.4.2 Coupling to Bosonic Modes -- 4.5 Two-Particle Green's Functions and Correlation Functions -- 4.5.1 Diagrammatic Representation of the Two-Particle Green's Function -- 4.5.2 Correlation Functions -- 4.6 Coulomb Interaction and Proper and Improper Response Functions -- 4.7 Irreducible Vertices and the Bethe-Salpeter Equations -- 4.7.1 Particle-Hole Channel -- 4.7.2 Particle-Particle Channel -- 4.7.3 Self-energy and Irreducible Vertices -- 4.8 The Luttinger-Ward Functional -- 4.8.1 Thermodynamic Potential -- 4.9 Ward-Takahashi Identities -- 4.9.1 Ward-Takahashi Identity for the Heat Density -- 4.10 Conserving Approximation Schemes -- 4.10.1 Conserving Hartree-Fock Approximation -- 4.10.2 Conserving GW Approximation -- 4.11 Luttinger's Theorem -- 4.11.1 Validity Conditions for Luttinger's Theorem -- 4.11.2 Luttinger's Theorem in Presence of Quasiparticles and in Periodic Systems -- Problems -- 5 Landau's Fermi Liquid Theory -- 5.1 Emergence of Quasiparticles Reexamined -- 5.2 Manipulating the Bethe-Salpeter Equation -- 5.2.1 A Lengthy but Necessary Preliminary Calculation.
5.2.2 Interaction Vertex and Density-Vertices -- 5.3 Linear Response Functions -- 5.3.1 Response Functions of Densities Associated to Conserved Quantities -- 5.4 Thermodynamic Susceptibilities -- 5.4.1 Charge Compressibility -- 5.4.2 Spin Susceptibility -- 5.4.3 Specific Heat -- 5.5 Current-Current Response Functions -- 5.5.1 Thermal Response -- 5.5.2 Coulomb Interaction -- 5.6 Mott Insulators with a Luttinger Surface -- 5.7 Luttinger's Theorem and Quasiparticle Distribution Function -- 5.7.1 Oshikawa's Topological Derivation of Luttinger's Theorem -- 5.8 Quasiparticle Hamiltonian and Landau-Boltzmann Transport Equation -- 5.8.1 Landau-Boltzmann Transport Equation for Quasiparticles -- 5.8.2 Transport Equation in Presence of an Electromagnetic Field -- 5.9 Application: Transport Coefficients with Rotational Symmetry -- 6 Brief Introduction to Luttinger Liquids -- 6.1 What Is Special in One Dimension? -- 6.2 Interacting Spinless Fermions -- 6.2.1 Bosonized Expression of the Non-interacting Hamiltonian -- 6.2.2 Bosonic Representation of the Fermi Fields -- 6.2.3 Operator Product Expansion -- 6.2.4 Non-interacting Green's Functions and Density-Density Response Functions -- 6.2.5 Interaction -- 6.2.6 Interacting Green's Functions and Correlation Functions -- 6.2.7 Umklapp Scattering -- 6.2.8 Behaviour Close to the K=1/2 Marginal Case -- 6.3 Spin-1/2 Heisenberg Chain -- 6.4 The One-Dimensional Hubbard Model -- 6.4.1 Luttinger Versus Fermi Liquids -- Problems -- 7 Kondo Effect and the Physics of the Anderson Impurity Model -- 7.1 Brief Introduction to Scattering Theory -- 7.1.1 General Analysis of the Phase-Shifts -- 7.2 The Anderson Impurity Model -- 7.2.1 Non Interacting Impurity -- 7.2.2 Hartree-Fock Approximation -- 7.3 From the Anderson Impurity Model to the Kondo Model -- 7.3.1 The Emergence of Logarithmic Singularities and the Kondo Temperature.
7.3.2 Anderson's Poor Man's Scaling -- 7.4 Noziéres's Local Fermi Liquid Theory -- 7.4.1 Ward-Takahashi Identity -- 7.4.2 Luttinger's Theorem and Thermodynamic Susceptibilities -- Problems.
Record Nr. UNISA-996499865103316
Fabrizio Michele  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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Feynman diagram techniques in condensed matter physics / / Radi A. Jishi, California State University [[electronic resource]]
Feynman diagram techniques in condensed matter physics / / Radi A. Jishi, California State University [[electronic resource]]
Autore Jishi Radi A. <1955->
Pubbl/distr/stampa Cambridge : , : Cambridge University Press, , 2013
Descrizione fisica 1 online resource (xiv, 400 pages) : digital, PDF file(s)
Disciplina 530.4/1
Soggetto topico Feynman diagrams
Many-body problem
Condensed matter
ISBN 1-107-23631-2
1-107-34425-5
1-107-34800-5
1-107-34175-2
1-107-65533-1
1-139-17777-X
1-107-34906-0
1-107-34550-2
1-107-02517-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto A brief review of quantum mechanics -- Single-particle states -- Second quantization -- The electron gas -- A brief review of statistical mechanics -- Real-time Green's and correlation functions -- Applications of real-time Green's functions -- Imaginary-time Green's and correlation functions -- Diagrammatic techniques -- Electron gas : a diagrammatic approach -- Phonons, photons, and electrons -- Superconductivity -- Nonequilibrium Green's function -- Appendix A : Second quantized form of operators -- Appendix B : Completing the proof of Dzyaloshinski's rules -- Appendix C : Lattice vibrations in three dimensions -- Appendix D : Electron-phonon interaction in polar crystals.
Record Nr. UNINA-9910464673103321
Jishi Radi A. <1955->  
Cambridge : , : Cambridge University Press, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Feynman diagram techniques in condensed matter physics / / Radi A. Jishi, California State University [[electronic resource]]
Feynman diagram techniques in condensed matter physics / / Radi A. Jishi, California State University [[electronic resource]]
Autore Jishi Radi A. <1955->
Pubbl/distr/stampa Cambridge : , : Cambridge University Press, , 2013
Descrizione fisica 1 online resource (xiv, 400 pages) : digital, PDF file(s)
Disciplina 530.4/1
Soggetto topico Feynman diagrams
Many-body problem
Condensed matter
ISBN 1-107-23631-2
1-107-34425-5
1-107-34800-5
1-107-34175-2
1-107-65533-1
1-139-17777-X
1-107-34906-0
1-107-34550-2
1-107-02517-6
Classificazione SCI055000
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto A brief review of quantum mechanics -- Single-particle states -- Second quantization -- The electron gas -- A brief review of statistical mechanics -- Real-time Green's and correlation functions -- Applications of real-time Green's functions -- Imaginary-time Green's and correlation functions -- Diagrammatic techniques -- Electron gas : a diagrammatic approach -- Phonons, photons, and electrons -- Superconductivity -- Nonequilibrium Green's function -- Appendix A : Second quantized form of operators -- Appendix B : Completing the proof of Dzyaloshinski's rules -- Appendix C : Lattice vibrations in three dimensions -- Appendix D : Electron-phonon interaction in polar crystals.
Record Nr. UNINA-9910789315603321
Jishi Radi A. <1955->  
Cambridge : , : Cambridge University Press, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Feynman diagram techniques in condensed matter physics / / Radi A. Jishi, California State University
Feynman diagram techniques in condensed matter physics / / Radi A. Jishi, California State University
Autore Jishi Radi A. <1955->
Edizione [1st ed.]
Pubbl/distr/stampa Cambridge : , : Cambridge University Press, , 2013
Descrizione fisica 1 online resource (xiv, 400 pages) : digital, PDF file(s)
Disciplina 530.4/1
Soggetto topico Feynman diagrams
Many-body problem
Condensed matter
ISBN 1-107-23631-2
1-107-34425-5
1-107-34800-5
1-107-34175-2
1-107-65533-1
1-139-17777-X
1-107-34906-0
1-107-34550-2
1-107-02517-6
Classificazione SCI055000
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto A brief review of quantum mechanics -- Single-particle states -- Second quantization -- The electron gas -- A brief review of statistical mechanics -- Real-time Green's and correlation functions -- Applications of real-time Green's functions -- Imaginary-time Green's and correlation functions -- Diagrammatic techniques -- Electron gas : a diagrammatic approach -- Phonons, photons, and electrons -- Superconductivity -- Nonequilibrium Green's function -- Appendix A : Second quantized form of operators -- Appendix B : Completing the proof of Dzyaloshinski's rules -- Appendix C : Lattice vibrations in three dimensions -- Appendix D : Electron-phonon interaction in polar crystals.
Record Nr. UNINA-9910809541703321
Jishi Radi A. <1955->  
Cambridge : , : Cambridge University Press, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Field theoretical methods in many-body systems / D.A. Kirzhnits ; translated by A.J. Meadows and edited by D.M. Brink
Field theoretical methods in many-body systems / D.A. Kirzhnits ; translated by A.J. Meadows and edited by D.M. Brink
Autore Kirzhnits, D.A.
Pubbl/distr/stampa Oxford : Pergamon, 1967
Descrizione fisica xvi, 394 p. : ill. ; 23 cm.
Altri autori (Persone) Meadows, A.J.
Brink, D.M.
Collana International series of monographs in natural philosophy ; 8
Soggetto topico Many-body problem
Classificazione 53.1.4
53.1.64
53.3.1
53.4.16
530.14'4
QC174.5.K5713
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991000944359707536
Kirzhnits, D.A.  
Oxford : Pergamon, 1967
Materiale a stampa
Lo trovi qui: Univ. del Salento
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