Kubo formula

About: Kubo formula is a research topic. Over the lifetime, 1052 publications have been published within this topic receiving 34322 citations.

Many-Particle Physics

Abstract: 1. Introductory Material.- 1.1. Harmonic Oscillators and Phonons.- 1.2. Second Quantization for Particles.- 1.3. Electron - Phonon Interactions.- A. Interaction Hamiltonian.- B. Localized Electron.- C. Deformation Potential.- D. Piezoelectric Interaction.- E. Polar Coupling.- 1.4. Spin Hamiltonians.- A. Homogeneous Spin Systems.- B. Impurity Spin Models.- 1.5. Photons.- A. Gauges.- B. Lagrangian.- C. Hamiltonian.- 1.6. Pair Distribution Function.- Problems.- 2. Green's Functions at Zero Temperature.- 2.1. Interaction Representation.- A. Schrodinger.- B. Heisenberg.- C. Interaction.- 2.2. S Matrix.- 2.3. Green's Functions.- 2.4. Wick's Theorem.- 2.5. Feynman Diagrams.- 2.6. Vacuum Polarization Graphs.- 2.7. Dyson's Equation.- 2.8. Rules for Constructing Diagrams.- 2.9. Time-Loop S Matrix.- A. Six Green's Functions.- B. Dyson's Equation.- 2.10. Photon Green's Functions.- Problems.- 3. Green's Functions at Finite Temperatures.- 3.1. Introduction.- 3.2. Matsubara Green's Functions.- 3.3. Retarded and Advanced Green's Functions.- 3.4. Dyson's Equation.- 3.5. Frequency Summations.- 3.6. Linked Cluster Expansions.- A. Thermodynamic Potential.- B. Green's Functions.- 3.7. Real Time Green's Functions.- Wigner Distribution Function.- 3.8. Kubo Formula for Electrical Conductivity.- A. Transverse Fields, Zero Temperature.- B. Finite Temperatures.- C. Zero Frequency.- D. Photon Self-Energy.- 3.9. Other Kubo Formulas.- A. Pauli Paramagnetic Susceptibility.- B. Thermal Currents and Onsager Relations.- C. Correlation Functions.- Problems.- 4. Exactly Solvable Models.- 4.1. Potential Scattering.- A. Reaction Matrix.- B. T Matrix.- C. Friedel's Theorem.- D. Phase Shifts.- E. Impurity Scattering.- F. Ground State Energy.- 4.2. Localized State in the Continuum.- 4.3. Independent Boson Models.- A. Solution by Canonical Transformation.- B. Feynman Disentangling of Operators.- C. Einstein Model.- D. Optical Absorption and Emission.- E. Sudden Switching.- F. Linked Cluster Expansion.- 4.4. Tomonaga Model.- A. Tomonaga Model.- B. Spin Waves.- C. Luttinger Model.- D. Single-Particle Properties.- E. Interacting System of Spinless Fermions.- F. Electron Exchange.- 4.5. Polaritons.- A. Semiclassical Discussion.- B. Phonon-Photon Coupling.- C. Exciton-Photon Coupling.- Problems.- 5. Electron Gas.- 5.1. Exchange and Correlation.- A. Kinetic Energy.- B. Direct Coulomb.- C. Exchange.- D. Seitz' Theorem.- E. ?(2a).- F. ?(2b).- G. ?(2c).- H. High-Density Limit.- I. Pair Distribution Function.- 5.2. Wigner Lattice and Metallic Hydrogen.- Metallic Hydrogen.- 5.3. Cohesive Energy of Metals.- 5.4. Linear Screening.- 5.5. Model Dielectric Functions.- A. Thomas-Fermi.- B. Lindhard, or RPA.- C. Hubbard.- D. Singwi-Sjolander.- 5.6. Properties of the Electron Gas.- A. Pair Distribution Function.- B. Screening Charge.- C. Correlation Energies.- D. Compressibility.- 5.7. Sum Rules.- 5.8. One-Electron Properties.- A. Renormalization Constant ZF.- B. Effective Mass.- C. Pauli Paramagnetic Susceptibility.- D. Mean Free Path.- Problems.- 6. Electron-Phonon Interaction.- 6.1 Frohlich Hamiltonian.- A. Brillouin-Wigner Perturbation Theory.- B. Rayleigh-Schrodinger Perturbation Theory.- C. Strong Coupling Theory.- D. Linked Cluster Theory.- 6.2 Small Polaron Theory.- A. Large Polarons.- B. Small Polarons.- C. Diagonal Transitions.- D. Nondiagonal Transitions.- E. Dispersive Phonons.- F. Einstein Model.- G. Kubo Formula.- 6.3 Heavily Doped Semiconductors.- A. Screened Interaction.- B. Experimental Verifications.- C. Electron Self-Energies.- 6.4 Metals.- A. Phonons in Metals.- B. Electron Self-Energies.- Problems.- 7. dc Conductivities.- 7.1. Electron Scattering by Impurities.- A. Boltzmann Equation.- B. Kubo Formula: Approximate Solution.- C. Kubo Formula: Rigorous Solution.- D. Ward Identities.- 7.2. Mobility of Frohlich Polarons.- A. Single-Particle Properties.- B. ??1 Term in the Mobility.- 7.3. Electron-Phonon Interactions in Metals.- A. Force-Force Correlation Function.- B. Kubo Formula.- C. Mass Enhancement.- D. Thermoelectric Power.- 7.4. Quantum Boltzmann Equation.- A. Derivation of the Quantum Boltzmann Equation.- B. Gradient Expansion.- C. Electron Scattering by Impurities.- D. T2 Contribution to the Electrical Resistivity.- Problems.- 8. Optical Properties of Solids.- 8.1. Nearly Free-Electron System.- A. General Properties.- B. Force-Force Correlation Functions.- C. Frohlich Polarons.- D. Interband Transitions.- E. Phonons.- 8.2. Wannier Excitons.- A. The Model.- B. Solution by Green's Functions.- C. Core-Level Spectra.- 8.3. X-Ray Spectra in Metals.- A. Physical Model.- B. Edge Singularities.- C. Orthogonality Catastrophe.- D. MND Theory.- E. XPS Spectra.- Problems.- 9. Superconductivity.- 9.1. Cooper Instability.- 9.2. BCS Theory.- 9.3. Electron Tunneling.- A. Tunneling Hamiltonian.- B. Normal Metals.- C. Normal-Superconductor.- D. Two Superconductors.- E. Josephson Tunneling.- 9.4. Infrared Absorption.- 9.5. Acoustic Attenuation.- 9.6. Excitons in Superconductors.- 9.7. Strong Coupling Theory.- Problems.- 10. Liquid Helium.- 10.1. Pairing Theory.- A. Hartree and Exchange.- B. Bogoliubov Theory of 4He.- 10.2. 4He: Ground State Properties.- A. Off-Diagonal Long-Range Order.- B. Correlated Basis Functions.- C. Experiments on nk.- 10.3. 4He: Excitation Spectrum.- A. Bijl-Feynman Theory.- B. Improved Excitation Spectra.- C. Superfluidity.- 10.4. 3He: Normal Liquid.- A. Fermi Liquid Theory.- B. Experiments and Microscopic Theories.- C. Interaction between Quasiparticles: Excitations.- D. Quasiparticle Transport.- 10.5. Superfluid 3He.- A. Triplet Pairing.- B. Equal Spin Pairing.- Problems.- 11. Spin Fluctuations.- 11.1. Kondo Model.- A. High-Temperature Scattering.- B. Low-Temperature State.- C. Kondo Temperature.- 11.2. Anderson Model.- A. Collective States.- B. Green's Functions.- C. Spectroscopies.- Problems.- References.- Author Index.

Quantized Hall conductance in a two-dimensional periodic potential

Abstract: The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential $U$. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small $\frac{U}{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}$.

Relation between conductivity and transmission matrix

Abstract: The dc conductance 1 of a finite system with static disorder is related to its transmission matrix t by the simple relation 1 = (e /2nt) Tr(t t). This relation is derived from the Kubo formula and is valid for any number of scattering channels with or without time-reversal symmetry. Differences between various definitions of the conductance of a finite system are discussed. Some time ago Landauer' proposed that the dc conductance I' of noninteracting (spinless) electrons in a disordered medium in strictly one dimension is given by I' = (e'/2vrh) ~ r ~'/~ r (' where t and r are the transmission and reflection amplitudes. A relation of this kind, especially if it can be generalized to higher dimensions, is of great interest for at least two reasons. First, the cost of numerical computation may be greatly reduced compared with the conventional use of the Kubo formula. '~ Second, such a relation emphasizes the fundamental role of the conductance which is assumed to be the only relevant variable in a recent scaling theory treatment of the localization problem. " This point of view was discussed in a recent analysis of the conductivity of a one-dimensional (ID) chain9 in which Landauer's expression was used. The argument given by Landauer is a heuristic one and not easily generalized to higher dimensions.

From AdS/CFT correspondence to hydrodynamics

Abstract: We compute the correlation functions of R-charge currents and components of the stress-energy tensor in the strongly coupled large-N finite-temperature = 4 supersymmetric Yang-Mills theory, following a recently formulated minkowskian AdS/CFT prescription. We observe that in the long-distance, low-frequency limit, such correlators have the form dictated by hydrodynamics. We deduce from the calculations the R-charge diffusion constant and the shear viscosity. The value for the latter is in agreement with an earlier calculation based on the Kubo formula and absorption by black branes.

Heat transport in low-dimensional systems

Abstract: Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ∼ L α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no e...