A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.

Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems

The linear response theory has given a general proof of the fluctuation-dissipation theorem which states that the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium. This theorem may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion. In this generalized equation the friction force becomes retarded or frequency-dependent and the random force is no more white. They are related to each other by a generalized Nyquist theorem which is in fact another expression of the fluctuation-dissipation theorem. This point of view can be applied to a wide class of irreversible process including collective modes in many-particle systems as has already been shown by Mori. As an illustrative example, the density response problem is briefly discussed.

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The fluctuation-dissipation theorem

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

The Theory of a general quantum system interacting with a linear dissipative system

In previous papers we have formulated the theory of magnetostriction arising from single-ion crystal-field effects, for cubic crystals, and we have shown that the theory accounts extremely well for the temperature dependence of the magnetostriction in yttrium iron garnet. We here summarize that theory, extend it to arbitrary crystal symmetry, augment it by the inclusion of two-ion interactions, analyze the dependence on magnetic field strength (the "forced magnetostriction"), and discuss the totally symmetric component (which exhibits itself as an anomalous thermal expansion). The first part of this paper is concerned with the above matters, and the analysis is based entirely on symmetry considerations. It culminates in expressions relating the macroscopic magnetostriction coefficients to the product of microscopic magnetoelastic coupling constants and certain spin correlation functions. Only three such correlation functions appear, and all temperature and field dependence enters through these correlation functions. In the second part of the paper, we evaluate these correlation functions by various approximate theories: molecular field theory, a cluster theory, and the random-phase approximation. Applications to Dy and to EuS are cited, and a detailed application to Gd is given. In Gd the sign inversion of a particular magnetostriction coefficient, and its full temperature dependence, are accurately accounted for theoretically. The field dependence of the forced magnetostriction of Gd is also discussed, with special reference to the observed persistence of a pseudo-linearity slightly above the Curie temperature.

Magnetostriction, Forced Magnetostriction, and Anomalous Thermal Expansion in Ferromagnets

DESCRIPTION The only text to cover both thermodynamic and statistical mechanics--allowing students to fully master thermodynamics at the macroscopic level. Presents essential ideas on critical phenomena developed over the last decade in simple, qualitative terms. This new edition maintains the simple structure of the first and puts new emphasis on pedagogical considerations. Thermostatistics is incorporated into the text without eclipsing macroscopic thermodynamics, and is integrated into the conceptual framework of physical theory.

Thermodynamics and an Introduction to Thermostatistics, 2nd ed.

Statistical Mechanics and Field-Induced Phase Transitions of the Heisenberg Antiferromagnet

Irreversible Thermodynamics of Nonlinear Processes and Noise in Driven Systems

The electric breakdown strength of ionic crystals at low and moderate temperatures is calculated on the basis of von Hippel's low energy criterion. Fr\"ohlich's method of calculation, modified to take account of the electronic polarizability of the ions, is employed. The breakdown strength at $T=0\ifmmode^\circ\else\textdegree\fi{}$ is ${F}_{0}(\frac{\mathrm{volts}}{\mathrm{cm}})=134\ifmmode\times\else\texttimes\fi{}{10}^{6}{(\ensuremath{\hbar}{\ensuremath{\omega}}_{t})}_{\mathrm{ev}}[\frac{({\ensuremath{\epsilon}}_{s}\ensuremath{-}{\ensuremath{\epsilon}}_{0})}{{({\ensuremath{\epsilon}}_{s}\ensuremath{\epsilon}_{0}^{}{}_{}{}^{3})}^{\frac{1}{2}}}](\frac{{m}^{*}}{m})$ where ${(\ensuremath{\hbar}{\ensuremath{\omega}}_{t})}_{\mathrm{ev}}$ is the reststrahl energy in electron volts, ${\ensuremath{\epsilon}}_{s}$ and ${\ensuremath{\epsilon}}_{0}$ are the static and optical values of the dielectric constant, and $\frac{{m}^{*}}{m}$ is the ratio of the effective mass to the free electron mass. The breakdown strength increases slowly with increasing temperature. The lack of dependence of the breakdown on crystallographic orientation and the strong directional dependence of the breakdown paths are qualitatively accounted for.

Herbert B. Callen

Papers

Magnetostriction, Forced Magnetostriction, and Anomalous Thermal Expansion in Ferromagnets

Thermodynamics and an Introduction to Thermostatistics, 2nd ed.

Statistical Mechanics and Field-Induced Phase Transitions of the Heisenberg Antiferromagnet

Irreversible Thermodynamics of Nonlinear Processes and Noise in Driven Systems

Electric Breakdown in Ionic Crystals