A molecular dynamics study on a system of infinitely thin hard rods is reported. At low densities, rotational and translational diffusion is adequately described by the Enskog theory, but at high densities (${\rho }^{*}\gg 1$) large deviations are observed. For ${\rho }^{*}\gg 1$, the rotational diffusion constant ($D_r$) and the longitudinal translational diffusion constant ($D_{\parallel }$) are compared with scaling predictions. The molecular dynamics results confirm that $D_r\sim {{\rho }^{*}}^{-2\mathrm{}}$, and are consistent with a predicted divergence of $D_{\parallel }\sim {{\rho }^{*}}^{\frac{1}{2}}$.

The inner product of two states in Hilbert space is interpreted in terms of a relationship between two or more distinct physical systems. This point of view suggests a generalized notion of measurement, within which the familiar types of measurement occur as special cases. A variety of novel measuring procedures are described, which relate overcomplete sets of states for a given system to complete sets for some larger system (of which the smaller system forms a part).

A new relation is reported which quantitatively describes the fine structure of the chaotic region of period-doubling systems. The relation determines the onset of fundamental periods and of ergodic behavior. It involves bifurcation rates ${\gamma }_k$, which converge to a new universal constant $\gamma =2.948\mathrm{}05\dots$. This theory is in agreement with numerical determinations of ${\gamma }_k$.

An experiment gave results inconsistent with the simplest alternative to quantum gravity, the semiclassical Einstein equations. This evidence supports (but does not prove) the hypothesis that a consistent theory of gravity coupled to quantized matter should also have the gravitational field quantized.

The quantum limitations on measurements of the relative positions of the two mirrors in a Michelson gravity-wave detector are derived. The effects of intensity fluctuations in the two light beams and radiation pressure on the mirrors are modeled in a unified calculation. The radiation-pressure uncertainty in mirror position differs in general from earlier work, but gives agreement for coherent input light.

A neutron interferometer experiment testing the existence of an Aharonov-Bohm effect has been performed and no measurable phase shift has been found upon reversal of the enclosed magnetic flux. A positive result would have provided evidence for a breakdown in the standard minimal-coupling scheme for the electromagnetic interaction of a neutron. The sensitivity of the experiment sets the ratio of the Aharonov-Bohm effect for a neutron to that of a particle of charge $e$ to be less than 5×${10}^{-12\mathrm{}}$.

An exactly solvable model of an interface between coexisting phases in a modified planar lattice gas, or its magnetic equivalent, is described. The results reconcile the apparent conflict between intrinsic structure and capillary fluctuation theory. There are anomalously long-ranged correlations in the interface.

A lattice model for equilibrium polymerization which allows for loop polymers is presented with critical behavior described by $n=1\mathrm{}$, rather than $n\to 0$ predicted by the theory of Wheeler, Kennedy, and Pfeuty. The specific heat of sulfur above and below $T_c$ is consistent with Ising critical behavior.

We have measured the linear polarization correlation of the photons emitted in a radiative atomic cascade of calcium. A high-efficiency source provided an improved statistical accuracy and an ability to perform new tests. Our results, in excellent agreement with the quantum mechanical predictions, strongly violate the generalized Bell's inequalities, and rule out the whole class of realistic local theories. No significant change in results was observed with source-polarizer separations of up to 6.5 m.

A general theory of the interaction of superfluid helium with a gravitational field is developed within the framework of general relativity by using a covariant generalization of the Gross-Pitaevskii equation. The general relativistic Sagnac effect for the superfluid Josephson interferometer is obtained in the stationary case. The influence of a plane-polarized gravitational wave on a recently proposed superfluid gravitational antenna as well as a new antenna is determined.

A new type of compensated Penning trap with the ring electrode split into equal quadrants allows intense unshifted ion cyclotron resonances to be synchronously detected with very small relative linewidths (< 2×${10}^{-9\mathrm{}}$). By measuring the cyclotron frequencies of both protons and electrons in the same magnetic field (5 T) and the same trapping volume (<${10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$), a preliminary value of the mass ratio $\frac{m_p}{m_e}=1836.153\mathrm{}00\left(25\right)\mathrm{}$ is obtained with an accuracy that is more than four times greater than any previous direct measurement.

It is shown that a proper analytic continuation of eigenvalues of a special inhomogeneous eight-vertex system determines the "phases" and the spectrum of a one-dimensional fermion gas model, and thus provides a particular example of the long suspected connection between factorized $S$ matrices and lattice statistical systems.

It is rigorously proved that the continuum limits of Euclidean ${\varphi }_d^4$ lattice fields are free fields in $d>\mathrm{}4\mathrm{}$. An exact geometric characterization of criticality in Ising models is introduced, and used to prove other mean-field features for $d>\mathrm{}4\mathrm{}$ and hyperscaling in $d=2\mathrm{}$.

We study directed percolation in two dimensions. Critical properties, such as the threshold $p_c$ and the correlation length exponent $\nu$, depend on the direction $\varphi$ at which percolation is observed. We observe crossover from $\nu (\varphi =0)$ to $\nu \left(\varphi \ne 0\right)$; similar crossover is found when the probabilities assigned to vertical and horizontal bonds, $p_V$ and $p_H$, become unequal. For the case $p_H=1\mathrm{}$ we solved the problem exactly, obtaining $p_c\left(\varphi \right)={[1+cot(\frac{1}{4}\pi -\varphi \left)\right]}^{-1\mathrm{}}$, $\nu =2\mathrm{}$.

By giving an explicit example in one dimension, it is shown that by relaxing a condition on the ranges, at least two potentials can have the same scattering operator in some cases. The two potentials are local and do not support point eigenvalues. The implications for solutions of the Korteweg-de Vries equation are briefly discussed.

A path-integral method is developed for the calculation of the statistical properties of a class of dissipative mappings which exhibit strange attractors. Exact analytic results are derived for the low-order statistical moments. These nontrivial results are verified numerically.

Using a two-slit neutron interferometer, we have measured the shift of the interference pattern induced by the motion of a quartz rod. The measured shift is found to be in agreement with the quantum mechanical prediction derived from a relativity argument. Some peculiarities of the case of massive particles as compared with the classic Fizeau photon case are discussed.

We discuss the properties of an ideal relativistic Bose gas with nonzero chemical potential $\mu$ (i.e., with net charge) but differ from all previous discussions by including the effects of antiparticles. We obtain for the first time the relevant high-temperature expansion, emphasizing the constraint $\left|\mu \right|<~m$, and show that a box of massless particles can have a net charge even though $\mu =0\mathrm{}$. Finally, we discuss the properties of Bose-Einstein condensation for both massless and massive bosons in $d$ space dimensions.

A powerful, new extension of the Monte Carlo renormalization-group (MCRG) method is used to accurately determine the tricritical point and exponents in two very different two-dimensional models: an Ising antiferromagnet and a Blume-Capel model. We find four relevant tricritical eigenvalues which are essentially identical for both models. We also demonstrate that subtle warning signals appear in a standard Monte Carlo calculation when a second-order transition is being misinterpreted as first order.

It is shown that the same arguments which lead to black-hole evaporation also predict that a thermal spectrum of sound waves should be given out from the sonic horizon in transsonic fluid flow.