A theory of the low-frequency vibrational spectra in disordered systems is proposed and is based on accounting for small statistical fluctuations of the sound velocity. Long-range quasilocalized sound excitations of a circular nature are predicted. A circular excitation is localized during its lifetime inside an appropriate fluctuation that has the form of a thin tube bent into a ring. The density of states of such excitations estimated by the optimum fluctuation method depends exponentially on the frequency. The existence of a characteristic frequency is found at which the density of the quasilocalized states competes with that of phonons, providing a kind of anomaly in the total density of vibrational states. This frequency depends both on the correlation radius of the disorder and its amplitude. The theory predicts qualitatively a universal behavior of the density of vibrational states in various disordered systems possessing medium-range order.

A model of the transition from the orientationally disordered to the quadrupolar-glass (QG) phase of mixed alkali cyanide crystals is proposed. Starting from the semimicroscopic Hamiltonian constructed by Vollmayr, Kree, and Zippelius the effective Hamiltonian containing random long-ranged orientational interactions between ${\mathrm{CN}}^{\mathrm{-}}$ ions and their orientational coupling to the random local strain field has been obtained. The ${\mathrm{CN}}^{\mathrm{-}}$ ion is treated as a quadrupolar molecule and no restriction has been made to a finite number of spatial orientations of it. With the Sherington-Kirkpatrick approach the formula for the free energy has been derived. In the framework of the replica-symmetric theory the Landau expansion of the free energy up to third order in the QG Edwards-Anderson parameter has been performed in the absence of the random local strain field. This predicts a continuous QG transition. However, it is smeared out due to the influence of the random local strains, which in fact have a nonzero value. The elastic compliance has been calculated and it has been shown, that ${\mathit{T}}_{2\mathit{g}}$ orientational modes govern the softening of the elastic constant ${\mathit{C}}_{44}$ on approaching the QG transition point, whereas ${\mathit{E}}_{2\mathit{g}}$ modes are responsible for the much less pronounced temperature dependence of ${\mathit{C}}_{11}$ and ${\mathit{C}}_{12}$. This is in agreement with experimental data.

The behavior of crystalline α-quartz under hydrostatic pressure is studied via total-energy calculations based on the full-potential linearized augmented-plane-wave method, within the local-density approximation. By examining recent experimental data and our theoretical results, the structural properties of α-quartz near and above the transition to the amorphous state are determined. Our results indicate that the ${\mathrm{SiO}}_4$ tetrahedra distort, with a regular and slight decrease of the mean distance Si-O; the interpolyhedral Si-O-Si angles and the O-O distances decrease below the smallest value experimentally observed on ordered silicates, with a dramatic reduction of the structural voids. The oxygen lattice tends towards an ideal close-packed configuration, perhaps highly instable.

Constant-pressure molecular-dynamics simulations of rigid, infinitely long polyacetylene chains were performed for various temperatures and pressures. The experimentally observed anisotropic lattice thermal expansion and compressibility were qualitatively well reproduced by the simulations. The model lattice exhibits considerable jump diffusion along chain axes already at room temperature, with the onset of liquidlike diffusion above 400 K accompanied by orientational disorder of chain projections in the ab plane. The polarized vibrational density of states for E≤25 meV is in good agreement with G(E) spectra derived from inelastic incoherent neutron-scattering experiments. By analyzing different contributions to chain motions, peaks in G(E) at 3.5, ∼8, and ∼20 meV can be assigned to rigid-chain vibrations along the chain axis, vibrations in the ab plane, and chain librations, respectively.

We calculate the freqency correlation function in a disordered slab using the usual diagrammatic approximation and compare our results to numerical simulations. As long as the decay width of the system is much bigger than the Thouless energy the two methods agree. Once the decay width is of order of the Thouless energy discrepancies in the half-width of the correlation function as well as in the tail regions appear. This behavior indicates the importance of the decay width in determining transport properties of disordered systems.

As a crystal is disordered, a point may be reached where the typical mean free path of phonons is so short that the wavelength and mean free path are no longer sharp concepts, and the textbook phonon-gas model for thermal conductivity breaks down. This paper proposes an alternate theory for the disordered regime, and the subsequent paper implements the theory for a realistic model of amorphous silicon. The idea is that the dominant scattering is correctly described by a harmonic Hamiltonian, which is, in principle, transformable into a one-body problem of decoupled oscillators. From this the thermal conductivity can be exactly calculated by an analog of the Kubo-Greenwood formula for electrical conductivity of disordered metals. Anderson localization is correctly contained in this theory; localized states contribute no currents in harmonic approximation. What is required is an atomistic model with a large unit cell and periodic boundary conditions (to avoid undesired surface effects). The linear size of the model should be larger than the mean free paths of the dominant phonons. A Kubo formula and then a Kubo-Greenwood-type formula are derived for this problem. A ‘‘mode diffusivity’’ ${\mathit{D}}_{\mathit{i}}$ for the ith exact oscillator state is defined. The heat is carried by off-diagonal elements of the heat current operator, which have a nonzero contribution because the temperature gradient introduces nonzero off-diagonal elements of the density matrix 〈${\mathit{a}}_{\mathit{i}}^{\mathrm{°}}$${\mathit{a}}_{\mathit{j}}$〉. An effort is made to interpret these results physically. Schemes for implementing this formalism are discussed.

Numerical calculations of thermal conductivity κ(T) are reported for realistic atomic structure models of amorphous silicon with 1000 atoms and periodic boundary conditions. Using Stillinger-Weber forces, the vibrational eigenstates are computed by exact diagonalization in harmonic approximation. Only the uppermost 3% of the states are localized. The finite size of the system prevents accurate information about low-energy vibrations, but the 98% of the modes with energies above 10 meV are densely enough represented to permit a lot of information to be extracted. Each harmonic mode has an intrinsic (harmonic) diffusivity defined by the Kubo formula, which we can accurately calculate for ω>10 meV. If the mode could be assigned a wave vector k and a velocity v=∂ω/∂k, then Boltzmann theory assigns a diffusivity ${\mathit{D}}_{\mathbf{k}}$=1/3vl, where l is the mean free path. We find that we cannot define a wave vector for the majority of the states, but the intrinsic harmonic diffusivity is still well-defined and has a numerical value similar to what one gets by using the Boltzmann result, replacing v by a sound velocity and replacing l by an interatomic distance a. This appears to justify the notion of a minimum thermal conductivity as discussed by Kittel, Slack, and others. In order to fit the experimental κ(T) it is necessary to add a Debye-like continuation from 10 meV down to 0 meV.

The harmonic diffusivity becomes a Rayleigh ${\mathrm{\omega }}^{\mathrm{-}4}$ law and gives a divergent κ(T) as T→0. To eliminate this we make the standard assumption of resonant-plus-relaxational absorption from two-level systems (this is an anharmonic effect which would lie outside our model even if it did contain two-level systems implicitly). A reasonable fit and explanation then results for the behavior of κ(T) in all temperature regimes. We also study the effect of increasing the harmonic disorder by substitutional mass defects (modeling amorphous Si/Ge alloys). The additional disorder increases the fraction of localized states, but delocalized states still dominate. However, the diffusivity of the delocalized states is diminished, weakening our faith in any literal interpretation of the minimum conductivity idea.

During low-temperature impact-ionization breakdown in extrinsic germanium, quasiperiodic current oscillations arise spontaneously. If the two competing frequencies (strictly speaking, the corresponding oscillatory components) can be localized in two spatially separated regions of the sample, mode locking can hardly be observed. However, if the two frequencies can be detected all over the sample, the frequency ratio undergoes an exemplary mode-locking sequence under variation of a transverse magnetic field. We find that the mode lockings are in accordance with the Farey-tree configuration, originally predicted to hold for periodically driven systems.

For a quantum particle on a one-dimensional lattice, the dynamics under the influence of a time-dependent, white-noise potential is shown to differ significantly from the classical diffusive behavior. In particular, the square of the distance displaced from origin is proportional to ${\mathit{t}}^{0.5–0.6}$. The origin of this dispersive behavior is traced to the special properties of the force-force correlation function, which integrates to zero and has a magnitude varying as ${\mathit{t}}^{\mathrm{-}0.5}$. These characteristics are attributed to the continuous spread of the quantum wave packet as well as its interaction with the discrete lattice.

We have measured the ν=0→1 Raman-active vibron in HD to 120 GPa. We combine our results with previous work in ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ to study inter- and intramolecular coupling in solid hydrogen to megabar pressures. We find that a model potential composed of inter- and intramolecular parts may be used to explain experimental results over a large pressure range. On the other hand, analyzing the intramolecular coupling using a Morse-type effective pair potential yields results that seem unphysical. We have also observed that HD molecules are stable against formation of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ to the highest pressures studied.

Electron-spin-resonance data taken at 9 GHz for hydrogen atoms in tritiated solid ${\mathrm{H}}_2$, HD, ${\mathrm{D}}_2$, D-T, and ${\mathrm{T}}_2$ are presented. Both linewidths and longitudinal relaxation times have been measured simultaneously with J=1 and hydrogen-atom concentrations. Data are presented to show that the line shapes can be inhomogeneous. Linewidth calculations using the weak dipolar interaction and hyperfine interaction are presented. Both predict Gaussian lines, and agreement is poor with the measured line shapes that are more often closer to Lorenzian. The Gaussian theories may be useful only for a few data points taken with high J=1 concentration and at high temperature. A dilute-spin theory for atom-atom interactions when little J=1 hydrogen is present, fails to work as well. The best line-shape agreement is obtained with a combination of J=1 and atom concentrations, both to the half power. ${\mathrm{D}}_2$ fails conspicuously with every approach. The longitudinal relaxation times appear constant at 0.1–1 s except at low J=1 concentrations, where the relaxation times increase. The electric-quadrupole mechanism is postulated for low J=1 concentrations, but it does not show the expected J=1 dependence. No information on ‘‘hidden’’ atoms is forthcoming from these data, but their presence is still a possibility.

A theory of the influence of isotopic impurities on phonon frequencies and bandwidths, based on the formalism of the retarded Green’s functions, is presented. The theory takes into account both harmonic and anharmonic processes in the crystal and yields a proper self-energy that includes impurity-activated contributions depending on the concentration of the impurities and on a parameter λ defined as the ratio of the mass difference to the mass of the impurity atoms. The theory is developed up to second order in the parameter λ and in the concentration of impurities. Central to the theory is the technique of averaging the anharmonic-phonon propagators over the ensemble of impurity configurations. This gives rise to a proper self-energy that includes harmonic and anharmonic contributions to both the phonon shift and damping. The most important result is that processes linear in the quartic anharmonicity, that in the pure crystal contribute only to the phonon shift, in the presence of isotopic impurities give rise also to a contribution to the damping.

We describe an approach for computing the conductivity associated with long-range hopping on energetically disordered lattices. Using a numerically exact supercell procedure we compute the distribution ${\mathrm{\rho }}_{\mathit{L}}$(γ) of block conductances ${\gamma }_{\mathit{L}}$ associated with conducting cubes of edge length L that are randomly chosen from the disordered system of interest. This distribution of block conductances is then used in a self-consistent numerical calculation to obtain the renormalized bulk conductivity. The approach displays a surprisingly fast approach to the infinite-system limit, allowing finite-size effects to be minimized. In this paper we use this approach to study transport in a series of binary lattices containing a random distribution of two enegetically inequivalent ions. Specific examples considered include variations of the nearest-neighbor site percolation problem, long-range hopping on more general binary lattices, and the trapping-to-percolation transition that occurs in such systems.

We propose a one-dimensional hydrogen-bonded chain model, where temperature is introduced using a variational form of the self-consistent-phonon-approximation method to evaluate the semiquantum free energy. The parameters of the model are chosen self-consistently and the hydrogen bond is described by a double Morse interaction. The behavior of the chain is studied with a defect and without one and the Peierls barrier is calculated. Introduction of an anharmonic O-O interaction results in slight qualitative changes.

A phonon instability of polaron excited states is investigated in the strong-coupling limit. This instability is connected with branching of solutions to the nonlinear polaron equation. It is shown by numerical calculations that the phonon instability leads to the decay of an excited spherically symmetric polaron state. As a result new asymmetric self-consistent states appear. This effect is analogous to the pseudo-Jahn-Teller effect and may be observed experimentally.

We report Raman- and neutron-scattering, infrared-transmission, and photoluminescence experiments in a series of isotopically enriched samples of Ge, including natural Ge and an alloy ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}_{0.5}^{}{}_{}{}^{}$ ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}_{0.5}^{}{}_{}{}^{}$. Emphasis is put on the study of disorder-induced effects on the phonon spectra. Results are compared to exhaustive theoretical calculations using the coherent-potential and self-consistent Born approximations. Reasonably good agreement is found between theory and experiment for the former. Data for the dependence of the energy of the ${\mathit{E}}_1$ interband electronic gap on isotopic mass are also presented.

We present an ab initio study of the electronic and magnetic structure of the antiferromagnetic state of ${\mathrm{MnF}}_2$ and ${\mathrm{NiF}}_2$. From the band structures of these two compounds we derive densities of states (DOS), electron densities, spin densities, electric-field gradients, and total energies. We use a simple molecular-orbital scheme to interpret the results. The internal coordinate u is determined by total-energy minimization for ${\mathrm{MnF}}_2$ and agrees well with experiment as well as with the calculated electric-field gradients or the electron densities. Recent spin-dependent x-ray-absorption spectra are interpreted in terms of partial DOS of the unoccupied Mn 4p states.

Some features common to many rare-earth intermetallic compounds with complex magnetic phase diagrams are explained using a realistic mean-field model, which takes into account the periodic-exchange-field and crystal-field effects which favor an easy magnetization axis, i.e.: (i) the change of an incommensurate or long-period commensurate structure near ${\mathit{T}}_{\mathit{N}}$ toward a simple commensurate one at low temperature, with and without intermediate structures of intermediate propagation vectors; (ii) the low-temperature metamagnetic process during which the high-temperature propagation vector(s) tend to be recovered; (iii) the trend for the propagation vectors to lock onto commensurate values, except near ${\mathit{T}}_{\mathit{N}}$. Exchange interactions alone are enough to account for these properties, the exact boundaries of the magnetic phase diagram being determined by the real variation of J(q) and crystal-field effects.

A spin-1 antiferromagnetic Heisenberg chain with a single-ion anisotropy ${\mathit{Dtsum}}_{\mathit{j}}$(${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$${)}^2$ is investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the ground state, the excitation spectrum, and the correlation functions are derived in a self-consistent-field approach. We find that the ground state is made of boson pairs and the correlation functions in the ground state decay exponentially. Two Haldane gaps due to the single-ion anisotropy are obtained and a transition at the critical value ${\mathit{D}}_{\mathit{c}}$=1 is shown in the lower Haldane gap and the correlation functions.

With the use of self-consistent spin-wave theory, the spin stiffness for the two-dimensional classical easy-plane ferromagnet is calculated. The Kosterlitz-Thouless transition temperature for the classical XY model is obtaind. The contribution of vortex-antivortex bound pairs to the central peak at low temperatures is discussed.