Using a neutron interferometer of the type first developed by Bonse and Hart for x rays, we have observed the effect of Earth's rotation on the phase of the neutron wave function. This experiment is the quantum mechanical analog of the optical interferometry observations of Michelson, Gale, and Pearson.

It is shown that the same two features that determine the structure of ordinary gravity and supergravity theories also determine the structure of conformal gravity. The relevant local gauge symmetry turns out to be the inhomogeneous Weyl group. The transformation laws of the fields follow from geometry. Some consequences of breaking the scale symmetry are briefly discussed.

We construct the manifold of zero-energy eigenstates for a nonrelativistic spin-½ particle moving in a plane in an external magnetic field $B\left(\overrightarrow{\mathrm{x}}\right)=\Sigma {n=0\mathrm{}}^N{\lambda }_n(\overrightarrow{\mathrm{x}}-{\overrightarrow{\mathrm{c}}}_n)$, with $\left\{{\lambda }_n\right\}$ and $\left\{{\overrightarrow{\mathrm{c}}}_n\right\}$ arbitrary reals and $\left\{k_n\right\}$ positive integers. For a given $B$ the ground state is infinitely degenerate and the manifold of eigenfunctions is parametrized by a point in $R^{2(2k_{max}+1)}$. For such $B$'s we prove paramagnetism with arbitrary external potential $V\left(\overrightarrow{\mathrm{x}}\right)$.

General covariance and maxium four-dimensional Yang-Mills gauge symmetry lead to these results: (1) Gravity is characterized by a dimensionless constant $F\sim {10}^{-19\mathrm{}}$; (2) the Newtonian force is always attractive; (3) space-time has a torsion; (4) gravitational spin-force between two protons is about ${10}^{19}$ times stronger than the corresponding Newtonian force. A possible experimental test is discussed.

Using a molecular-dynamics technique for the classical sine-Gordon chain, we have found that nonlinear breather modes give rise to two excitation branches. A low-frequency resonance is associated with the propagating envelope and a high-frequency peak with the internal oscillations.

A simplified method of applying a renormalization-group analysis to Monte Carlo simulations of general systems is presented and illustrated with applications to the Ising model and the three-state Potts model.

The kinetic theory of the fluctuations of a gas not in equilibrium is given and applied to light scattering. Unequal heights of the Brillouin lines are found in the presence of a temperature gradient.

Conduction by classical charge carriers is investigated for a one-dimensional system interrupted by barriers with a random distribution of activation energies. Under certain conditions the transport properties are dominated by disorder, and the model predicts an anomalous low-frequency conductivity $\sigma \left(\omega \right)\sim {(-i\omega )}^{\nu }$, with $\nu =\frac{(1-\frac{T}{T_m})}{(1+\frac{T}{T_m})}$, for $T<\mathrm{}{T}_m$, and a mobility transition at $T=T_m$. The model is shown to describe recent experiments on the one-dimensional superionic conductor hollandite (${\mathrm{K}}_{1.54}$${\mathrm{Mg}}_{0.77}$${\mathrm{Ti}}_{7.23}$${\mathrm{O}}_{16}$).

If scattering amplitudes are ordinary complex numbers (not quaternions) then there is a universal algebraic relationship between the six coherent cross sections of any three scatterers (taken singly and pairwise). A violation of this relationship would indicate either that scattering amplitudes are quaternions, or that the superposition principle fails. Some experimental tests are proposed, involving neutron diffraction by crystals made of three different isotopes, neutron interferometry, and $K_S$-meson regeneration.

The edge of the gap in the distribution of the Yang-Lee zeros is concluded to be a singular point of square-root type in all hierarchical models, in distinction to expectations based on renormalization-group arguments for short-range models in dimensions $d<\mathrm{}6\mathrm{}$.

We extend our previous method of proving the positive-mass conjecture to prove the positive-action conjecture of Hawking for asymptotically Euclidean metric. This result is crucial in proving the path integral convergent in the Euclidean quantum gravity theory.

Extremely sensitive readout of a stable "etalon of length" is achieved with laser frequency-locking techniques. Rotation of the entire electro-optical system maps any cosmic directional anisotropy of space into a corresponding frequency variation. We found a fractional length change $\frac{\Delta l}{l}=(1.5\mathrm{}\pm 2.5)\times {10}^{-15\mathrm{}}$, with the expected $P_2\left(cos\theta \right)$ signature. This null result represents a 4000-fold improvement on the best previous measurement of Jaseja et al.

A method is presented for generating stationary, axisymmetric, asymptotically flat, vacuum solutions of Einstein's equation with an arbitrary number of mass and angularmomentum parameters. As an example, a two-parameter asympotically flat solution, generalizing extreme Kerr, is generated from flat space. It is conjectured that the method, applied to the general static metric, can be used to generate all stationary, axisymmetric, asymptotically flat metrics.

The ambiguity in the Hamiltonian for systems with constraints is discussed, and a counter example is provided to a conjecture of Dirac, which has led previously to the identification of the system Hamiltonian as the extended Hamiltonian, $H_E$. The conjecture fails and $H_E$ also generates the wrong canonical equations; Dirac's test for identifying the Hamiltonian, however, leads to correct results for the example.

I present a class of vacuum metrics with a pair of commuting Killing vectors which do not possess the property of orthogonal transitivity. The solution is Petrov type II with expansion-, twist-, and shear-free geodesic rays and includes the van Stockum exterior metric as a limiting case.

A theory of gravity incorporating the concept of spontaneous symmetry breaking is proposed. It is suggested that the same symmetry-breaking mechanism is responsible for breaking a unified gauge theory into strong, weak, and electromagnetic interactions.

The energy of a linearly perturbed system is shown to verify a nonlinear first-order differential equation in the semiclassical limit. Solutions of this equation are compared to the exact energies, for a quartic oscillator.

We report a theroetical prediction of a new feature in the spectrum of light scattered from a fluid in a nonequilibrium stationary state with a temperature gradient. The spectrum is not symmetric in the frequency shift and the Brillouin components have different intensities. The phenomenon is linked to the breaking of time-reversal symmetry and to the appearance of a static correlation function between momentum and number densities which is zero in equilibrium, but has a $\frac{1}{k^2}$ dependence in the stationary state. We suggest a light scattering experiment by means of which these predictions can be verified.

We report the large-$\mathcal{r}$ and small-$\mathcal{r}$ expansions of the one-particle reduced density $\stackrel{\mathrm{`}}{\mathrm{m}}$atrix $\rho \left(\mathcal{r}\right)$ of a system of impenetrable bosons in one dimension at zero temperature. These expansions were derived from an exact calculation of $\rho \left(\mathcal{r}\right)$ to be reported elsewhere. We find that the large-$\mathcal{r}$ expansion of $\rho \left(\mathcal{r}\right)$ contains oscillatory terms which we relate to the analytic structure of the momentum density function $n\left(k\right)\mathrm{}$.

By choosing a suitable probability distribution the decay of an unstable state of a macroscopic system can be described deterministically; the effects of fluctuations then show up in the initial probability density. There is no need to distinguish an initial linear and diffusive regime from a later deterministic one.