High-resolution thermal-conductivity and heat-capacity studies on the same sample have been carried out near the smectic-$A$-hexatic-$B$ transition of $n-\mathrm{hexyl}-4\text{'}-n-\mathrm{pentyloxybiphenyl}-4-\mathrm{carboxylate}$ (65OBC). A power-law fitting with background contribution to the thermal conductivity anomaly leads to a dynamic critical exponent $a=0.51\mathrm{}$ and a ratio of critical amplitudes $\frac{{\Lambda }^{+}}{{\Lambda }^{-}}=0.93\mathrm{}$. We will discuss our results on the basis of a dynamic scaling. The thermal diffusivity shows a pronounced drop near the transition, which clearly demonstrates critical slowing down of the thermal fluctuations. mal fluctuations.

Dipolar and quadrupolar susceptibility measurements are reported for the molecular glass system ${\left(\mathrm{KBr}\right)}_{1-x}{\left(\mathrm{KCN}\right)}_x$ covering a wide range of frequencies. The results allow a direct comparison of the dipolar and quadrupolar anomalies and demonstrate unambiguously that the freezing in of the dipolar and quadrupolar degrees of freedom occurs at different temperatures.

The dynamical structure factor of highly ordered and disordered states of amorphous Ge has been obtained from inelastic-neutron-scattering measurements. The results indicate significant changes in the phonon density of states, due to bond-angle-distribution variations. The modified structure factor, $G(Q,E)\mathrm{}$, indicates damped oscillatory behavior that is in very good agreement with the bond-coherency model of Weaire and Alben. Low-$Q$ deviations suggest coherency effects beyond first neighbors.

On the basis of a calculation using the Landau theory of cholesterics, we propose that the anomalous blue phase III is characterized by a novel structure with broken icosahedral symmetry. Methods for confirming this structure assignment are suggested. This phase is likely to be an unambiguous example of a thermodynamically stable phase with long-range quasicrystalline ordering.

The energetics of icosahedral ordering in cholesteric liquid crystals are studied within the Landau mean-field approximation, in an attempt to describe the blue fog (blue phase III). We expand the free energy of a quasicrystalline phase in the high-chirality limit (coherence length much greater than pitch), and find that although it is energetically competitive with the cubic blue phases, no vertex-edge icosahedral phase is ever favored in this regime.

We develop a new method to calculate from first principles the electronic structure of infinite nonperiodic systems of atoms. The calculation is performed with use of atomic pseudopotentials and a basis of atomic Gaussian wave functions. We solve the Hartree-Fock self-consistent equations in a cluster-Bethe lattice system. Electron correlation is partially included in second-order perturbation approximation. The formalism is successfully applied to a study of hydrogenated amorphous silicon.

The vibronic coupling strengths of the two barrier-separated ${\mathrm{In}}^{2+}$ states in Cd${\mathrm{F}}_2$ are found to differ by more than 1 order of magnitude, thus implying a large difference in localization of these two states. This observation gives the first direct evidence of the validity of the general Toyozawa model of impurity self-trapping: A single defect may indeed bind an electron on either a very localized or a delocalized orbit. These two states, although very close in energy, are separated by a vibronic barrier, which causes metastable effects.

We have made an $a$ priori theoretical study of the potential-energy surfaces for KCa${\mathrm{F}}_3$ and RbCa${\mathrm{F}}_3$, and have examined the relative stability of the various lower-symmetry structures generated from the cubic perovskite phase by "rotations" of the Ca${\mathrm{F}}_6$ octahedra. A completely new ground state was discovered which, when included in the sequence of energy levels, allows us to give a full account both qualitatively and, in the case of RbCa${\mathrm{F}}_3$, quantitatively of the phase transition sequences in both systems.

We have measured the exciton (triplet) recombination (fusion, annihilation) characteristics of naphthalene-doped microporous materials. This technique yields the dynamic (spectral, fracton) dimension of the embedded naphthalene structure or the effective random-walk dimension of the porous network. Temperature studies separate the energetic and geometric features of the pore space. The geometric dynamic (spectral) dimensions are mostly between 1 and 2, i.e., fractal-like, and are consistent with previous results on the static (fractal or Euclidean) dimensions of the porous Vycor glass samples.

The tunneling conductance of junctions formed on thin films of Al in contact with films of the ferromagnetic semiconductor EuO implies that such composites behave like BCS superconductors with internal magnetization. In a magnetic field $B$ applied in the plane of the films, the superconducting quasiparticle density of states shows a splitting $2\mu (B^{*}+B)$, where $B^{*}$ can be greater than $B$ by more than a tesla. The critcal field of composite films is reduced by approximately $B^{*}$ compared to that of identical Al films without EuO. The observed $B^{*}$ is of the same magnitude as $\mu {}_0{}^{}{}_{}{}^{}M$, the magnetization of EuO.

A conventional fermion interferometer, in which the fermions enter only one of the two input ports, can achieve a phase sensitivity $\Delta \phi =\frac{1}{\sqrt{n}}$, where $n$ is the total number of fermions which have passed through the interferometer. Here it is shown that by injection of fermions into both input ports the phase sensitivity can approach $\frac{1}{n}$ provided that the fermions in the two input beams are suitably correlated.

A new approach to Preisach's hysteresis model, which emphasizes its phenomenological nature and mathematical generality, is briefly described. Then the theorem which gives the necessary and sufficient conditions for the representation of actual hysteresis nonlinearities by Preisach's model is proven. The significance of this theorem is that it establishes the limits of applicability of this model.

Instabilities in the electrical conductivity of barium sodium niobate crystals are studied with ac and dc fields. Phase portraits, Poincaré sections, and return maps are constructed from measured signals in the quasiperiodic state. We show that the dynamical behavior of the system can be modeled by a 1D circle map. Mode locking is observed in the system prior to the transition to chaos; the mode-locked intervals exhibit a devil's staircase behavior.

A generalized $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. It is shown that even for a finite number of spins the model has a phase transition in the limit $n\to \infty$. The transition features a specific-heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also discussed.

We show that the Hamiltonian of the 1D Hubbard model commutes with a one-parameter family of transfer matrices of a new 2D classical model corresponding to two coupled six-vertex models. Central to this result is a new local algebraic relation, a generalization of the (infinitesimal) startriangle relation.

A spinorial time-space ${\mathfrak{G}}_N$ that supports a Kaluza-Klein theory of gauge potentials can be made from $N$-component spinors of $\mathrm{SL}\mathrm{}(N,C)\mathrm{}$ in the way that the Minkowskian manifold (an ${\mathfrak{G}}_2$) is made from two-component spinors of $\mathrm{SL}\mathrm{}(2,C)\mathrm{}$. ${\mathfrak{G}}_N$ has dimension $n=N^2$ and fundamental form det $\left(k_{\Sigma \dot{\Sigma }}\right)=0\mathrm{}$ of degree $N$, not 2. ${\mathfrak{G}}_N$ unifies the photon and graviton with gauge quanta of all integer spins $s$ with $2<s<N$.

An approach to anomalies from anomalous vacuum expectation values is proposed. This method is useful to derive not only the conformal anomaly, the chiral anomaly, and the gravitational anomaly but also the supercurrent anomaly at one-loop order. Calculations are carried out for the $N=1\mathrm{}$ self-interacting Wess-Zumino model in flat space-time and for the $N=1\mathrm{}$ supersymmetric Yang-Mills theory in graviton and gravitino background fields.

We derive a set of invariant quantities in fermion-mass matrices, independent of one's weak-eigenstate basis, the vanishing of which is both necessary and sufficient for $\mathrm{CP}$ invariance. Our method is applied to the standard single-Higgs-doublet SU(2) ⊗ U(1) model with an arbitrary number of fermion generations.

A polarized proton beam in a $\mathrm{PP}$ or a $P\overline{P}$ collider permits a normalization-independent determination of the quark polarization inside a hadron via the forward-backward asymmetry in $W^{\pm }$ decay. For an unpolarized beam one still obtains useful information about antiquark distributions.

The decay channels of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}*$ excited to energies between 10 and 1800 MeV are sampled by a microcanonical Monte Carlo calculation; i.e., the total energy, momentum, baryon number, and charge are strictly conserved quantities. From samples of about 2 × ${10}^6$ complete events, various averages are calculated, such as the number $N_c$ of charged fragments, the number of prompt and of evaporated neutrons, the temperrature, and the multiplicity of heavy fragments. The distributions of the multiplicity $N_c$ and of the temperature $T$ are calculated as well.