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電子ブック
ＥＢ
1. Density Functional Theory
Eberhard Engel, Reiner M. Dreizler, Gyula O. H. Katona, Gábor Fejes Tóth, László Lovász
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2011
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Introduction / 1：
Foundations of Density Functional Theory: Existence Theorems / 2：
Hohenberg-Kohn Theorem / 2.1：
Degenerate Ground States / 2.2：
Variational Equation, Interacting v-Representability, Functional Differentiability / 2.3：
Fractional Particle Numbers, Derivative Discontinuity / 2.4：
Spin-Polarized Systems / 2.5：
Current Density Functional Theory / 2.6：
Excited States: Part 1 / 2.7：
Effective Single-Particle Equations / 3：
Kohn-Sham Equations / 3.1：
Noninteracting v-Representability / 3.2：
Degenerate Kohn-Sham Ground States / 3.3：
Janak's Theorem, Fractional Particle Numbers / 3.4：
Kohn-Sham Equations for Spin-Polarized Systems / 3.5：
Interpretation of Kohn-Sham Eigenvalues: Relation to Ionization Potential, Fermi Surface and Band Gap / 3.6：
Ionization Potential / 3.6.1：
Fermi Surface / 3.6.2：
Band Gap / 3.6.3：
Kohn-Sham Equations of Current Density Functional Theory / 3.7：
Exchange-Correlation Energy Functional / 4：
Definition of Exact Exchange within DFT / 4.1：
Variant (a): Kohn-Sham Perturbation Theory / 4.2：
Variant (b): Adiabatic Connection / 4.2.2：
Local Density Approximation (LDA) / 4.3：
Exchange / 4.3.1：
Correlation: High-Density Limit / 4.3.2：
Correlation: Low-Density Limit / 4.3.3：
Correlation: Interpolation Between High- and Low-Density Regime / 4.3.4：
Density Functional: Local Density Approximation (LDA) / 4.3.5：
Spin-Polarized Electron Gas: Local Spin-Density Approximation (LSDA) / 4.3.6：
Nonlocal Corrections to the LDA / 4.4：
Weakly Inhomogeneous Electron Gas / 4.4.1：
Complete Linear Response / 4.4.2：
Gradient Expansion / 4.4.3：
Generalized Gradient Approximation (GGA) / 4.5：
Momentum Space Variant / 4.5.1：
Real Space Variant / 4.5.2：
Combination of Momentum and Real Space Variants / 4.5.3：
Semi-Empirical Construction of GGAs / 4.5.4：
Merits and Limitations of GGAs / 4.5.5：
Weighted Density Approximation (WDA) / 1.4.6：
Self-Interaction Corrections (SIC) / 4.7：
Meta-GGA (MGGA) / 4.8：
LDA+U / 4.9：
Virial Theorems / 5：
Scaling Behavior of Energy Contributions / 5.1：
Conventional Virial Theorem / 5.2：
DFT Virial Theorem / 5.3：
Hellmann-Feynman Theorem / 5.4：
Orbital Functionals: Optimized Potential Method / 6：
Motivation / 6.1：
Atomic Negative Ions / 6.1.1：
Dispersion Forces / 6.1.2：
Strongly Correlated Systems / 6.1.3：
Third Generation of DFT / 6.1.4：
Derivation of OPM Integral Equation / 6.2：
Compact Notation / 6.2.1：
Direct Functional Derivative / 6.2.2：
Total Energy Minimization / 6.2.3：
Invariance of Density / 6.2.4：
Exact Relation's Based on OPM Integral Equation / 6.2.5：
Krieger-Li-Iafrate Approximation (KLI) / 6.2.6：
OPM in Case of Degeneracy / 6.2.7：
Exchange-Only Results / 6.3：
First-Principles Implicit Correlation Functionals / 6.4：
Kohn-Sham Perturbation Theory / 6.4.1：
Kohn-Sham-Based Random Phase Approximation / 6.4.2：
Interaction Strength Interpolation (ISI) / 6.4.3：
Model-Based Orbital-Dependent Exchange-Correlation Functionals / 6.5：
Self-Interaction Corrected LDA / 6.5.1：
Colle-Salvetti Functional / 6.5.2：
Meta-GGA / 6.5.3：
Global, Screened and Local Hybrid Functionals / 6.5.4：
Analysis of Orbital-Dependent Correlation Functionals / 6.6：
Dispersion Force / 6.6.1：
Correlation Energy / 6.6.2：
Correlation Potential / 6.6.3：
Orbital-Dependent Representation of 2-Particle Density / 6.7：
Time-Dependent Density Functional Theory / 7：
Runge-Gross Theorem / 7.1：
Time-Dependent Kohn-Sham Equations / 7.2：
Exchange-Correlation Action: Adiabatic Local Density Approximation and Beyond / 7.3：
Time-Dependent Linear Response / 7.4：
Spin-Polarized Time-Dependent Density Functional Theory / 7.5：
Excited States: Part II / 7.6：
Relativistic Density Functional Theory / 8：
Notation / 8.1：
Field Theoretical Background / 8.2：
Existence Theorem / 8.3：
Relativistic Kohn-Sham Equations / 8.4：
Towards a Workable RDFT Scheme: No-pair Approximation / 8.5：
No-pair RDFT / 8.6：
Variants of RDFT / 8.7：
Relativistic Exchange-Correlation Functional: Concepts and Illustrative Results / 8.8：
Relativistic Implicit Functionals: Optimized Potential Method / 8.8.1：
Relativistic Local Density Approximation / 8.8.2：
Relativistic Generalized Gradient Approximation / 8.8.4：
Further Reading / 8.8.5：
Functionals and the Functional Derivative / A：
Definition of the Functional / A.1：
Functional Derivative / A.2：
Calculational Rules / A.3：
Variational Principle / A.4：
Second Quantization in Many-Body Theory / B：
N-Particle Hilbert Space / B.1：
Realization in First Quantized Form / B.1.1：
Formal Representation / B.1.2：
Fock Space / B.2：
Creation and Annihilation Operators / B.2.1：
1-Particle Operators / B.2.2：
2-Particle Operators / B.2.3：
Scaling Behavior of Many-Body Methods / C：
Explicit Density Functionals for the Kinetic Energy: Thomas-Fermi Models and Beyond / D：
Asymptotic Behavior of Quasi-Particle Amplitudes / E：
Quantization of Noninteracting Fermions in Relativistic Quantum Field Theory / F：
Renormalization Scheme of Vacuum QED / G：
Relativistic Homogeneous Electron Gas / H：
Basic Propagators / H.1：
Response Functions / H.2：
Ground State Energy / H.3：
Ground State Four Current / H.4：
Renormalization of Inhomogeneous Electron Gas / I：
Gradient Corrections to the Relativistic LDA / J：
Gordon Decomposition / K：
Some Useful Formulae / L：
References
Index
Introduction / 1：
Foundations of Density Functional Theory: Existence Theorems / 2：
Hohenberg-Kohn Theorem / 2.1：
2.

電子ブック
ＥＢ
2. The Pursuit of Quantum Gravity
Cécile DeWitt-Morette, Bryce Seligman DeWitt, Cécile DeWitt-Morette, Reiner M. Dreizler, Eberhard Engel
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2011
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目次情報: 続きを見る
Introduction
Why Physics?
Why Quantum Gravity? Why Link Quantum Gravity and Bryce DeWitt's Memoirs?
Progress in Quantum Physics Since the Late Forties / I：
Functional Integration as a Major Technique in Quantum Physics / I.1：
The Geometry of Gauge Fields / I.2：
Classical Gauge Fields / I.2.1：
Quantum Gauge Fields / I.2.2：
Progress in Gravitation Since the Late Forties / II：
Numerical Relativity / II.1：
Classical Relativity / II.1.1：
Toy Models for Quantum Gravity / II.1.2：
Bryce DeWitt's Lectures on Relativity / II.2：
The 1973 Eclipse Expedition / II.3：
Quantum Gravity / III：
Ph.D. Thesis (Harvard 1950) / III.1：
Covariant Quantization vs. Canonical Quantization / III.2：
Dirac's Constrained Hamiltonian Dynamics / III.2.1：
The Wheeler-DeWitt Equation / III.2.2：
The "Trilogy" / III.2.3：
The Gravity Research Foundation Essay (1953) / III.3：
The Institute of Field Physics (1955-1964) / III.4：
Original Documents / III.4.1：
A Stone Thrown Into a Pool and Its Ripples / III.4.2：
The 1957 Chapel Hill Conference / III.5：
Everett's Theory and the "Many Worlds" Interpretation / III.6：
Everett's Theory Viewed / Bryce DeWittIII.6.1：
Relativity, Groups, and Topology / John WheelerIII.6.2：
Quantum Field Theory in Curved Spacetime / III.8：
Supermanifolds / III.9：
The Global Approach to Quantum Field Theory / III.10：
The Pursuit Goes On / III.11：
A Few Comments from Bryce DeWitt / IV：
Amateurs, Crackpots, Professionals, and Gravitation / IV.l：
Research Centers / IV.2：
Bibliography / V：
A Biographical Memoir by Steven Weinberg / V.1：
Publications / V.2：
Curriculum Vitae / V.3：
Archives Stored at the Center for American History / V.4：
About the Author
Name Index
Introduction
Why Physics?
Why Quantum Gravity? Why Link Quantum Gravity and Bryce DeWitt's Memoirs?
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