Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamics Brownian dynamics Quantum simulations Some applications Appendix A: Computers and computer simulation Appendix B: Reduced units Appendix C: Calculation of forces and torques Appendix D: Fourier transforms Appendix E: The gear predictor - corrector Appendix F: Programs on microfiche Appendix G: Random numbers References Index.

Computer Simulation of Liquids

The term ``sensitized luminescence'' in crystalline phosphors refers to the phenomenon whereby an impurity (activator, or emitter) is enabled to luminesce upon the absorption of light in a different type of center (sensitizer, or absorber) and upon the subsequent radiationless transfer of energy from the sensitizer to the activator The resonance theory of Forster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated The transfer mechanisms of importance are, in order of decreasing strength, the overlapping of the electric dipole fields of the sensitizer and the activator, the overlapping of the dipole field of the sensitizer with the quadrupole field of the activator, and exchange effects These mechanisms will give rise to ``sensitization'' of about 103−104, 102, and 30 lattice sites surrounding each sensitizer in typical systems The dependence of transfer efficiency upon sensitizer and activator concentrations and on temperature are discussed Application is made of the theory to experimental results on inorganic phosphors, and further experiments are suggested

A Theory of Sensitized Luminescence in Solids

The electronic properties of inversion and accumulation layers at semiconductor-insulator interfaces and of other systems that exhibit two-dimensional or quasi-two-dimensional behavior, such as electrons in semiconductor heterojunctions and superlattices and on liquid helium, are reviewed. Energy levels, transport properties, and optical properties are considered in some detail, especially for electrons at the (100) silicon-silicon dioxide interface. Other systems are discussed more briefly.

Electronic properties of two-dimensional systems

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

A review of dielectric data for a wide range of solids proves the existence of a remarkable ‘universality’ of frequency and time responses which is essentially incompatible with the multiplicity of currently accepted detailed interpretations. Certain unique features of the universal behaviour strongly suggest the dominant role of many-body interactions.

The ‘universal’ dielectric response

The semiclassical Franck‐Condon principle is shown to be related to the more rigorous (``exact'') quantum‐mechanical perturbation formula in the following ways: (1) the Franck‐Condon formula can be derived from the ``exact'' formula by using a mean value approximation or by neglecting certain commutators; (2) if the electric dipole moments are treated as approximately independent of position, the Franck‐Condon and the ``exact'' absorption (or emission) spectrum have the same zeroth, first, and second moments, i.e., the same integrated spectrum, mean absorption frequency, and breadth; (3) the errors in higher moments than the second become relatively unimportant at high temperatures. If the electron‐nuclear interaction is sufficiently strong the errors are unimportant even at absolute zero.The use of a quasi‐molecular description in a many particle problem is found to be possible only if the masses or stiffnesses are allowed to be temperature dependent.A detailed analysis is made of the case in which the e...

The Franck‐Condon Principle and Its Application to Crystals

Here we show and deduce the T-matrix and a general multiple scattering formulation which can be adapted to acoustics, electromag-netism, and elasticity. For details on each specific physical medium see the other documents.

Multiple scattering of waves

A general theory of stochastic transport in disordered systems has been developed. The theory is based on a generalization of the Montroll-Weiss continuous-time random walk (CTRW) on a lattice. Starting from a general mobility formalism, specialized $\stackrel{\mathrm{\ifmmode\acute\else\textasciiacute\fi{}}}{\mathrm{t}}$o hopping conduction, an exact expression for the conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ for the CTRW process is derived. The frequency dependence of $\ensuremath{\sigma}(\ensuremath{\omega})$ is determined by the Fourier transform of the zeroth and second spatial moments of the function $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}},t)$, which is equal to the probability per unit time that the displacement and time between hops is $\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$, $t$. The conductivity corresponding to characteristically different types of hopping distributions is discussed, as well as the basic approximation in adopting a CTRW on a lattice to transport in disordered solids.

Stochastic Transport in a Disordered Solid. I. Theory

The multiple scattering of waves interacting with a system of particles is treated by a self-consistent approach. Scattering processes are described by operators that permit anisotropy, absorption, and creation. The scattering system may be randomly, partially, or completely ordered.The propagation constant ${k}^{\ensuremath{'}}$ of the coherent wave in the scatterer medium differs from the vacuum constant $k$ by ${({k}^{\ensuremath{'}})}^{2}={k}^{2}+4\ensuremath{\pi}ncf({\mathbf{k}}^{\ensuremath{'}},{\mathbf{k}}^{\ensuremath{'}})$, where $n$ is the scatterer density and $f$ is an operator whose matrix elements $f(\mathbf{b},\mathbf{a})$ represent the scattering amplitude in direction b for a wave incident in direction a on a single scatterer bound by the forces of its neighbors. The parameter $c$, defined by $cf({\mathbf{k}}^{\ensuremath{'}},{\mathbf{k}}^{\ensuremath{'}})=\ensuremath{\int}\mathrm{exp}(\ensuremath{-}i{\mathbf{k}}^{\ensuremath{'}}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{r})f\ifmmode\times\else\texttimes\fi{}{\ensuremath{\psi}}_{e}(\mathbf{r})d\mathbf{r}$, is a measure of the ratio of the effective field ${\ensuremath{\psi}}_{e}(\mathbf{r})$ to the average field.An integral equation is found for ${\ensuremath{\psi}}_{e}(\mathbf{r})$ with the help of a "quasi-crystalline" approximation. A variational expression is then found for $c$ that becomes exact for point scatterers.A comparison is made of finite and infinite scattering systems. The extinction theorem is proven. The macroscopic viewpoint is found to be applicable to small systems whose size is large compared to the scatterer potential range, and the range of scatterer position correlations.

Multiple scattering of waves. ii. the effective field in dense systems

In a previous paper, the authors have developed a general theory of stochastic transport in disordered systems. In the present paper, the theory is applied, in detail, to a prototype of transport in a disordered system - impurity conduction in semiconductors. The complete frequency dependence of the real and imaginary part of the conductivity is calculated. In particular, the calculation details the transition from an ${\ensuremath{\omega}}^{s}$ dependence to essentially dc behavior (at a finite frequency), where $s\ensuremath{\sim}0.6\ensuremath{-}0.8$, depending on temperature and concentration. The theoretical results for frequency, temperature, and concentration dependence of the conductivity are shown to be in good agreement with the measurements of Pollak and Geballe (PG). In addition, the ac conductivity data of PG interpreted with the present theory yield experimental evidence for the existence of two-channel hopping in $n$-type Si.

Stochastic Transport in a Disordered Solid. II. Impurity Conduction

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