The dynamic Jahn-Teller effect provides a simple mechanism for inverting the ordering of the J=0,2 levels of the two equivalent holes in a neutral double acceptor or an exciton bound at a neutral acceptor. Whereas Hund’s rule places the J=2 level below J=0, Jahn-Teller coupling to E and/or ${\mathit{T}}_2$ vibrational modes tends to shift J=0 below J=2, while splitting J=2 into its ${\mathrm{\Gamma }}_3$ and ${\mathrm{\Gamma }}_5$ components. Alternative proposed explanations involving central-cell, Stark, and strain effects fail to introduce the attractive interaction needed to offset the holes’s Coulomb repulsion.

We present the first calculation of the self-trapped hole in a-${\mathrm{SiO}}_2$ that exhibits strong localization on one oxygen atom. This calculation was performed using both semiempirical and ab initio molecular orbital methods applied to finite clusters of atoms. The self-trapping is accompanied by a network distortion in which the two nearest-neighbor silicon atoms relax away from the self-trapped hole site along the Si-O bond directions. Our calculated ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ hyperfine interactions are in very good agreement with experiment.

We consider the magnetic field dependence of the chemical potential for parabolically confined quantum dots in a strong magnetic field. Approximate expressions based on the notion that the size of a dot is determined by a competition between confinement and interaction energies are shown to be consistent with exact diagonalization studies for small quantum dots. Fine structure is present in the magnetic field dependence which cannot be explained without a full many-body description and is associated with ground-state level crossings as a function of confinement strength or Zeeman interaction strength. Some of this fine structure is associated with precursors of the bulk incompressible states responsible for the fractional quantum Hall effect.

Collective charge transport is studied in one- and two-dimensional arrays of small normal-metal dots separated by tunneling barriers. At temperatures well below the charging energy of a dot, disorder leads to a threshold for conduction which grows linearly with the size of the array. For short-ranged interactions, one of the correlation length exponents near threshold is found from a novel argument based on interface growth. The dynamical exponent for the current above threshold is also predicted analytically, and the requirements for its experimental observation are described.

We use a functional integral formulation to study the finite temperature crossover from cooperative Cooper pairing to independent bound state formation and condensation. We show the inadequacy of mean field results for normal state properties obtained at the saddle point level as the coupling increases. The importance of quantum (temporal) fluctuations is pointed out and an interpolation scheme for ${\mathit{T}}_{\mathit{c}}$ is derived from this point of view. The time-dependent Ginzburg-Landau (TDGL) equation near ${\mathit{T}}_{\mathit{c}}$ is shown to describe a damped mode in the BCS limit, and a propagating one in the Bose limit. A singular point is identified at intermediate coupling where a simple TDGL description fails.

We obtain the V-I characteristics of the type-II superconductors for thin film by numerically solving the time-dependent Ginzburg-Landau equation coupled with the Maxwell equation in the two-dimensional region. We observe a sequence of pulses in the time development of the measured voltage, leading to intense energy dissipation in superconductors. We show that these voltage pulses are related to the penetration and annihilation of vortices at the boundary and the annihilation of two merging vortices with opposite sign.

We show that, in fully oxidized ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ c-axis oriented films, the changes induced in the angular and field dependence of the magnetoresistivity ${\mathrm{\rho }}_{\mathit{a}\mathit{b}}$ by increasing the temperature towards ${\mathit{T}}_{\mathit{c}}$ are similar to those caused by a lowering in oxygen content. This remarkable behavior can be interpreted as due to a crossover from a three-dimensional to a two-dimensional system as T approaches ${\mathit{T}}_{\mathit{c}}$. Moreover, our critical current data mimic the behavior observed by Qi Li et al. in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$/(${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$)${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ multilayers, suggesting the possibility that chain planes are superconducting.

Orbital Hartree-Fock and the local spin density approximations to exchange are compared. The self-exchange intergrals calculated from the Hartree-Fock approximation are far larger than those calculated from the local spin density approximation. We suggest that, in metals where the exchange integrals are well shielded, a suitable functional for exchange may be obtained by scaling the orbital Hartree-Fock approximation to the local spin density approximation while retaining the stronger orbital dependence. Application to Fe and US produces good agreement with measurements.

A class of Hubbard models with random hopping is examined as models of strongly correlated electrons in disordered systems. In the limit of large spatial dimensionality the problem is reduced to solving an ensemble of self-consistently determined Anderson impurity models. Even at intermediate correlation, disorder-induced local moment formation occurs, leading to a diverging specific heat coefficient inside the metallic phase. For stronger correlation, the system undergoes a metal-insulator transition where the dc conductivity abruptly drops to zero, displaying minimum metallic conductivity.

The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the ‘‘infinite avalanche’’ first disappears, are described by mean-field theory. We expand the critical exponents about mean-field theory, in 6-ε dimensions, to first order in ε. Despite ε=3, the values obtained agree reasonably well with the numerical values in three dimensions.

The interaction energy between emulsion droplets of micron and submicron size is theoretically studied. The role of the droplet deformability is considered in details and the equilibrium configuration of a doublet of droplets is determined. It is shown that the attractive interactions may lead to formation of a planar film between two colliding droplets. This deformation is particularly important at high electrolyte concentration and low interfacial tension. The radial distribution function, which can be used for determination of thermodynamic properties of emulsions, is calculated taking into account the droplet deformability.

We present a discrete, stochastic model for wind formed ripples in sand, which are observed to increase in size through mergers and seemingly approach an asymptotic spatial scale. The model is shown to predict (1) a logarithmic increase in pattern scale with time, (2) a proportionality between the microscopic discrete scale (sand grain diameter) and the macroscopic pattern scale (ripple height), and (3) a lack of scale separation. The implications are that growth and apparent stabilization of scale both can be explained by a single mechanism, and that the evolution of wind ripples and other physical systems of this type cannot be modeled by either deterministic methods or spatial continuum methods.

We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-order method.

The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.

We study the head-on collision of two equal-mass, nonrotating black holes. We consider various cases, from holes surrounded by a common horizon to holes separated by about 20M, where M is the mass of each hole. The wave forms and energy output are computed, showing that normal modes of the final black hole are clearly excited. We also estimate analytically the total gravitational radiation emitted, considering tidal heating of horizons and other effects. The analytic calculations, perturbation theory, and strong-field, nonlinear numerical calculations agree very well with each other.

Nucleon-nucleon scattering lengths are calculated by QCD sum rules. The calculation is based on the observation that the coefficient of the second-order pole term of the nucleon correlation function in nucleon is proportional to the nucleon-nucleon scattering length at the threshold. By applying Borel sum rules, we express the scattering length in terms of the expectation values of the quark-gluon field operators with respect to the one-nucleon state. The scattering lengths calculated are in qualitative agreement with the experiment. It is shown that in the linear density approximation the nucleon mass shift in nuclear matter is related to the nucleon-nucleon scattering length by δ${\mathit{M}}_{\mathit{N}}$=-(3π/2${\mathit{M}}_{\mathit{N}}$)(${\mathit{a}}_{\mathit{N}\mathit{N}}^1$+${\mathit{a}}_{\mathit{N}\mathit{N}}^3$)ρ.

A QCD-based treatment of projectile size fluctuations is used to compute inelastic diffractive cross sections ${\mathrm{\sigma }}_{\mathrm{diff}}$ for coherent hadron-nuclear processes. We find that fluctuations near the average size give the major contribution to the cross section with < few % contribution from small size configurations. The computed values of ${\mathrm{\sigma }}_{\mathrm{diff}}$ are consistent with the limited available data. The importance of coherent diffraction studies for a wide range of projectiles for high energy Fermilab fixed target experiments is emphasized. The implications of these significant color fluctuations for relativistic heavy ion collisions are discussed.

Differences between longitudinal and transverse two-proton correlation functions, consistent with finite lifetime effects, are observed for central ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$${+}^{45}$Sc collisions at E/A=80 MeV. The correlations between two protons emitted with low total momenta are consistent with emission from a source of Gaussian radius ${\mathit{r}}_0$≊4.7±0.3 fm and characteristic lifetime τ≊25±15 fm/c.

Dynamics of scattering in the classical model of α-cluster nuclei is studied in terms of transport theory. Behavior typical for hyperbolic chaotic scattering is found, which results in an exponential decay of the survival probability. This allows a determination of the unitarity deficit of the S matrix and thus the probability for compound-nucleus formation.

We present a calculation of the probability density for the excitation to the molecular continuum of ${\mathrm{HeT}}^{+}$ following the β decay of ${\mathit{T}}_2$, pertinent to the investigation of chemical effects in the neutrino mass experiments. The relevant transition amplitude has been obtained by means of a novel technique that avoids the explicit calculation of the continuum states of ${\mathrm{HeT}}^{+}$, and delivers the properly normalized probability density which includes both the background and resonant scattering contributions. We found two distinct sharp resonances at 75 eV below the end point of β spectrum where excess count rate has been observed in the recent neutrino mass experiment.