Consideration of a new class of interactions is proposed. These contain certain velocity-dependent terms which lead to confined systems by not permitting scattering. The relativistic two-body system is discussed as an example. Applications to quark-quark interactions are conceivable.

If black-hole formation and evaporation can be described by a superscattering operator which is $\mathrm{CPT}$ invariant, then it can be described by an $S$ matrix which maps pure initial states into pure final states. Thus black holes may be in principle no more unpredictable than other quantum phenomena.

Closed-form solution for the superspace connections of extended supergravity in terms of supervielbeine are given for arbitrary values of $N$, and deSitter parameter $e$. A reduction procedure from the Riemannian geometry is used to deduce the desired solutions.

It is shown that electromagnetic effects of a vector potential on a charged particle confined to a region $R$ (multiply or simply connected) are completely determined by field strengths in $R$, if the potential obeys certain conditions. Such potentials are adequate in experiments purporting to show Aharonov-Bohm effect. Therefore these experiments have not established effects of inaccessible fields.

The transport of electrons or excitations on a lattice randomly occupied by guests is considered. The equation governing the transport in any configuration is assumed to be the master equation. A projection operator technique is used to derive the exact equation governing the transport averaged over all configurations, which can be written as either a generalized master equation or the continuous-time random-walk equations (CTRW), establishing the correctness of the CTRW for these problems.

Studies of the adiabatic order-parameter susceptibility near symmetry-breaking phase transitions show that the ratio $\frac{{\chi }_S\mathrm{}\left(t\right)\mathrm{}}{{\chi }_S\mathrm{}(-t)\mathrm{}}$ (in the limit $t\to 0^{+}$), and the proportion of the order-parameter spectral intensity associated with the thermal diffusion mode (in the limit $t\to 0^{-}$), are universal. The universal quantities are tabulated and discussed in the light of experiments on structural phase transitions, with particular emphasis on the dielectric properties of ferroelectrics and the scattering properties of ordered phases. New experiments are suggested.

A close connection between Griffiths-Pearce "peculiarities" in position-space renormalization-group transformations and singularities in the free energies of systems with quenched random fields is pointed out. For a large class of weight functions the recurrence relations for the coupling constants of a nonrandom Ising system exhibit singularities where there is a phase transition in a related system with a random field.

Consider the statistical mechanics model on the $\nu$-dimensional lattice with nearest-neighbor interaction and single spin distribution given by $\lambda {(q^2-1)}^2$, $\lambda >0\mathrm{}$. The strong-coupling region $\lambda \to \infty$ is studied, and it is shown that in the high-temperature region there is an expansion of this model in powers of ${\lambda }^{-1\mathrm{}}$ which is asymptotic to the Ising model ($\lambda =\infty$) to any order.

A ring of tightly torsion-coupled, overdamped pendulums is subject to fluctuations and to a static applied torque. Over a wide range of forces, motion in this system occurs through the nucleation of a kink and antikink pair, their subsequent separation through the driving force, and eventual annihilation by collision with other kinks. This picture is used to calculate the mean angular pendulum velocity as a function of applied torque.

The positive-mass conjecture states that for a nontrivial isolated physical system, the total energy, which includes contributions from both matter and gravitation, is positive. This assertion has been demonstrated in the important case when the space-time admits a maximal slice. Here this assumption is removed and the general mass conjecture is demonstrated. Also the topology of all possible asymptotically flat space-times satisfying the local energy condition is determined.

This Letter investigates the conditions for Bose-Einstein condensation of an ideal relativistic Bose gas in different spatial dimensions. It is shown that the thermodynamical properties of the critical particle density are qualitatively different for massive and massless relativistic Bose particles.

It is discovered that the 1-eV positrons formed on an MgO-coated moderator with use of positrons from a ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$ source are polarized with degree of polarization $P={0.22}_{-0.02\mathrm{}}^{+0.04\mathrm{}}$. Improved design could increase $P$ to 0.40 with a flux of ${10}^5$-${10}^6$/sec. Applications of this discovery are discussed.

Renormalization-Group methods are used to calculate the critical distribution functions for large groups of ordering coordinates in two- and three-dimensional systems undergoing structural phase transitions. In two dimensions the distribution function shows clear evidence of well-defined clusters of precursor order, and cluster walls: The asymptotic collective behavior is always that of an order-disorder rather than a displacive system. In three dimensions the order-disorder component of the asympototic behavior is markedly weaker.

A Van de Graaff accelerator facility has been used as a supersensitive mass spectrograph in a search for free $+\frac{1}{3}\mathrm{}\left|e\right|\mathrm{}$ and $+\frac{2}{3}\mathrm{}\left|e\right|\mathrm{}$ charged ions in helium gas. No such ions were found at a level of sensitivity better than 1 part in 3.9× ${10}^{14}$ He atoms. The mass ranges spanned were 0.13 to 7.5 amu for $+\frac{1}{3}\mathrm{}\left|e\right|\mathrm{}$ ions and 0.27 to 15.0 amu for $+\frac{2}{3}\mathrm{}\left|e\right|\mathrm{}$ ions.

Molecular-dynamics simulations of the two-dimensional, classical electron gas yield indications for the existence of a self-diffusion constant, in contrast to the case of shortrange interactions. The velocity autocorrelation function exhibits marked oscillations in the strong-coupling regime. In order to avoid the Ewald summations of the Coulomb interactions in a periodic system, the electrons are confined on a spherical surface.

The quantum one-dimensional transverse Ising model with an imaginary longitudinal field is studied at $T=0\mathrm{}$ using a real-space renormalization-group method. Evaluation is made of the real part of the ground-state longitudinal magnetization which is related to the Yang-Lee distribution of zeros of the partition function for the two-dimensional classical Ising model. The edge exponents are found as $\sigma =-0.25\mathrm{}\pm 0.05$ and $\eta =-1.0\mathrm{}\pm 0.02$, in agreement with series expansion estimates.

The statistical mechanics of the interface between two discrete thermodynamic phases is studied in terms of a field $f$ which describes the deviation of the interface from planar. Exploiting the dynamical Euclidean invariance of the Hamiltonian of the field $f$, we construct $\epsilon$ expansions for Ising-like critical behavior in $1+\epsilon$ dimensions, with a critical temperature of order $\epsilon$, Scaling functions for the interface profile and width in a pinning potential are obtained.

$\frac{1}{f}$ noise has been predicted for simple physical systems that exhibit certain singularities in the fluctuation weighting function. We have produced a "quasi" singularity in the light-intensity pattern by focusing a laser beam with a cylindrical lens. The spectral density of the light scattered off polystyrene microspheres flowing through this region followed a $\frac{1}{f}$ dependence, as predicted. Other beam patterns gave the predicted noise spectra, including a $\frac{sin{\left(\pi f\tau \right)}^2}{{\left(\pi f\tau \right)}^2}$ spectral shape for flow past a slit.

A generalization of the Niemeijer-van Leeuwen renormalization-group transformation treating disordered cells of spins as vacancies is introduced and applied to the two-dimensional $q$-state Potts model. Finite-lattice approximations yield the changeover from continuous to first-order phase transitions predicted by Baxter but not observed in previous renormalization-group calculations. Exact results are conjectured for the tricritical exponents of dilute Potts models.

We present numerical estimates of the Hausdorff dimension $D$ of the largest cluster and its "backbone" in the percolation problem on a square lattice as a function of the concentration $p$. We fine that $D$ is an approximately linear function of $p$ in the region near $p=p_c (\simeq 0.59)$ with a dimension about equal to that of a self-avoiding walk when $p=0.455\mathrm{}$. The dimension of the backbone, or biconnected part, of the largest cluster equals that of the self-avoiding walk when $p\simeq p_c$. At $p=p_c$ the dimension of the largest cluster equals the anomalous dimension introduced by Stanley et al.