Book contents
- Frontmatter
- Contents
- Preface
- 1 Outline
- 2 Pair correlation function and structure factor of ions
- 3 Thermodynamics
- 4 Electron screening and effective ion-ion interactions
- 5 Interionic forces and structural theories
- 6 Statistical mechanics of inhomogeneous systems and freezing theory
- 7 Electronic and atomic transport
- 8 Hydrodynamic limits of correlation functions and neutron scattering
- 9 Critical behaviour
- 10 Electron states, including critical region
- 11 Magnetism of normal and especially of expanded liquid metals
- 12 Liquid-vapour surface
- 13 Binary liquid-metal alloys
- 14 Two-component theory of pure liquid metals
- 15 Shock-wave studies
- 16 Liquid hydrogen plasmas and constitution of Jupiter
- Appendices
- 2.1 Fluctuation theory derivation of S(0) in terms of compressibility
- 3.1 Percus-Yevick hard sphere solution for direct correlation function
- 3.2 Weeks-Chandler-Andersen (WCA) approximation to structure factor
- 5.1 Pressure dependence of pair function related to three-particle correlations
- 5.2 Conditions to be satisfied by thermodynamically consistent structural theories
- 5.3 Gaussian core model and Kirkwood decoupling of triplet correlations
- 5.4 Specific heats of liquids in terms of higher-order correlation functions
- 5.5 Inversion of measured structure, constrained by pseudopotential theory, to extract ion-ion interaction
- 6.1 Vacancy formation energy evaluated in a hot (model) crystal
- 6.2 Vacancy formation energy related to Debye temperature
- 7.1 Inverse transport theory for noninteracting electrons
- 8.1 Method of fluctuating hydrodynamics
- 8.2 Asymptotic behaviour of other Green-Kubo time correlation functions
- 8.3 Dynamics of S(k, ω) included through self-function Ss(k, ω)
- 8.4 Fourth moment theorem for dynamical structure factor
- 8.5 One-dimensional barrier crossing: Kramers' theory
- 8.6 Mode-coupling and velocity field methods
- 9.1 Ornstein-Zernike treatment of critical correlations
- 9.2 Homogeneity, scaling, and an introduction to renormalization group method
- 9.3 Compressibility ratios and thermal pressure coefficients of simple monatomic liquids from model equations of state
- 9.4 Mode coupling applied to critical behaviour
- 9.5 Proof of Wiedemann-Franz law up to metal-insulator transition for Fermi liquid model
- 10.1 Plasmon properties as function of phenomenological relaxation time
- 11.1 Heavy Fermion theory
- 13.1 Conformal solution theory: thermodynamics and structure
- 13.2 Results for concentration fluctuations from quasi-chemical approximation
- 13.3 Density profiles, direct correlation functions, and surface tension of liquid mixtures
- 13.4 Relation of surface segregation phenomenology to first-principles statistical mechanics
- 13.5 Long-time behaviour of correlation functions in binary alloys
- 13.6 Hydrodynamic correlation functions in a binary alloy
- 13.7 Metallic binary liquid-glass transition
- 13.8 Haeffner effect, electromigration, and thermal transport
- 13.9 Theory of disorder localization of noninteracting electrons
- 14.1 Phonon-plasmon model
- 14.2 Response functions for mass densities
- 14.3 Quantum hydrodynamic limit of two-component theory
- 14.4 Evaluation of transport coefficients
- 14.5 Electron-ion structure factor in a nonequilibrium situation
- 14.6 Relations between long-wavelength limit structure factors in binary metallic alloys
- 16.1 Integral equations for correlations in liquid metals, especially hydrogen
- 16.2 Quantum Monte Carlo calculations of ground state of solid hydrogen
- References
- Index
13.9 - Theory of disorder localization of noninteracting electrons
Published online by Cambridge University Press: 19 January 2010
- Frontmatter
- Contents
- Preface
- 1 Outline
- 2 Pair correlation function and structure factor of ions
- 3 Thermodynamics
- 4 Electron screening and effective ion-ion interactions
- 5 Interionic forces and structural theories
- 6 Statistical mechanics of inhomogeneous systems and freezing theory
- 7 Electronic and atomic transport
- 8 Hydrodynamic limits of correlation functions and neutron scattering
- 9 Critical behaviour
- 10 Electron states, including critical region
- 11 Magnetism of normal and especially of expanded liquid metals
- 12 Liquid-vapour surface
- 13 Binary liquid-metal alloys
- 14 Two-component theory of pure liquid metals
- 15 Shock-wave studies
- 16 Liquid hydrogen plasmas and constitution of Jupiter
- Appendices
- 2.1 Fluctuation theory derivation of S(0) in terms of compressibility
- 3.1 Percus-Yevick hard sphere solution for direct correlation function
- 3.2 Weeks-Chandler-Andersen (WCA) approximation to structure factor
- 5.1 Pressure dependence of pair function related to three-particle correlations
- 5.2 Conditions to be satisfied by thermodynamically consistent structural theories
- 5.3 Gaussian core model and Kirkwood decoupling of triplet correlations
- 5.4 Specific heats of liquids in terms of higher-order correlation functions
- 5.5 Inversion of measured structure, constrained by pseudopotential theory, to extract ion-ion interaction
- 6.1 Vacancy formation energy evaluated in a hot (model) crystal
- 6.2 Vacancy formation energy related to Debye temperature
- 7.1 Inverse transport theory for noninteracting electrons
- 8.1 Method of fluctuating hydrodynamics
- 8.2 Asymptotic behaviour of other Green-Kubo time correlation functions
- 8.3 Dynamics of S(k, ω) included through self-function Ss(k, ω)
- 8.4 Fourth moment theorem for dynamical structure factor
- 8.5 One-dimensional barrier crossing: Kramers' theory
- 8.6 Mode-coupling and velocity field methods
- 9.1 Ornstein-Zernike treatment of critical correlations
- 9.2 Homogeneity, scaling, and an introduction to renormalization group method
- 9.3 Compressibility ratios and thermal pressure coefficients of simple monatomic liquids from model equations of state
- 9.4 Mode coupling applied to critical behaviour
- 9.5 Proof of Wiedemann-Franz law up to metal-insulator transition for Fermi liquid model
- 10.1 Plasmon properties as function of phenomenological relaxation time
- 11.1 Heavy Fermion theory
- 13.1 Conformal solution theory: thermodynamics and structure
- 13.2 Results for concentration fluctuations from quasi-chemical approximation
- 13.3 Density profiles, direct correlation functions, and surface tension of liquid mixtures
- 13.4 Relation of surface segregation phenomenology to first-principles statistical mechanics
- 13.5 Long-time behaviour of correlation functions in binary alloys
- 13.6 Hydrodynamic correlation functions in a binary alloy
- 13.7 Metallic binary liquid-glass transition
- 13.8 Haeffner effect, electromigration, and thermal transport
- 13.9 Theory of disorder localization of noninteracting electrons
- 14.1 Phonon-plasmon model
- 14.2 Response functions for mass densities
- 14.3 Quantum hydrodynamic limit of two-component theory
- 14.4 Evaluation of transport coefficients
- 14.5 Electron-ion structure factor in a nonequilibrium situation
- 14.6 Relations between long-wavelength limit structure factors in binary metallic alloys
- 16.1 Integral equations for correlations in liquid metals, especially hydrogen
- 16.2 Quantum Monte Carlo calculations of ground state of solid hydrogen
- References
- Index
Summary
Although this volume is basically about metallic conductors, it is relevant to a discussion of electron states in disordered materials to give here some general background, plus relevant references, to the theory of localization of noninteracting electrons in a random potential.
The pioneering paper in this area was that of Anderson (1958) on the absence of diffusion in certain random lattices. But there was subsequently a lot of effort on this problem of noninteracting electrons in a static disordered potential before there was agreement on, at least, the answers to some important questions in this general area.
One might, at first sight, think it fruitful to compare the theory of electrons in disordered systems with the Bloch wave theory of the behaviour of electrons in a regular lattice. As Thouless (1979) emphasizes in his survey article, the theory of electrons in disordered systems is much more closely analogous to and owes much more to the theory of critical phenomena (see Chapter 9). In a sense then, developments in electron states in disordered systems awaited the synthesis of the theory of critical behaviour.
Following Thouless (1979), it is useful to group approaches into a number of areas, the first category being perturbative methods.
Perturbative methods
Anderson's original paper (1958) was based on the application of perturbation theory to a system that was strongly localized by a lot of disorder. In some ways, it resembles the Ursell-Mayer approach to phase transitions by examining the convergence of a high temperature perturbation series.
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- Liquid MetalsConcepts and Theory, pp. 444 - 446Publisher: Cambridge University PressPrint publication year: 1990