The frequency of a nuclear spin-flip ($\left|\Delta m_I\right|=1\mathrm{}$) transition in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ has been compared to the frequency of a hydrogen maser transition ($\left|\Delta F\right|=1\mathrm{}$, $\Delta m_F=0\mathrm{}$) to see if the relative frequencies depend on the orientation of the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions in space. The present null result represents a decrease in the limits set by Hughes and Drever on a spatial anisotropy by a factor of about 300.

We use a scaling analysis to estimate critical exponents for the electrical conductivity, elastic constants, and fluid permeability near the percolation threshold of a class of disordered continuum systems (Swiss-cheese models), where the transport medium is the space between randomly placed spherical holes. We find that the exponents are significantly larger than their counterparts in the standard discrete-lattice percolation networks, except for the case of electrical conductivity in two dimensions, where they are equal.

We show that states of systems which, in a very general sense, are approximately localized at time $t=0\mathrm{}$ in a finite region, with exponentially bounded tails outside, violate Einstein causality at later times. Implications are discussed.

The dielectric-plasma transition of the two-dimensional Coulomb gas, suitably mapped onto a delocalization transition, is investigated by molecular-dynamics simulations. The threshold temperature $T_1$ for electrical conduction falls well below the temperature $T_2$ associated with a marked peak in the specific heat; $T_2$ is close to the mean-field prediction for the Kosterlitz-Thouless transition, $\frac{k_{\mathrm{B}}{T}_2}{e^2}=\frac{1}{4}$.

It is shown that the entropy of a rotating, charged black hole is, in senses made precise in the paper, (i) the logarithm of the number of quantum mechanically distinct ways that the hole could have been made, and (ii) the logarithm of the number of configurations that the hole's "atmosphere," as measured by stationary observers, could assume in the presence of its background noise of acceleration radiation. In addition, a proof is given of the generalized second law of thermodynamics.

The equation of state of the fluid phase of the classical hard-sphere system in infinitely many dimensions has been obtained exactly. Only the first two virial coefficients are nonvanishing. The upper bound for the coefficients of the Mayer series for nonnegative interaction potentials is reached by this system.

We present evidence that hydrogen dissolved in metallic alloys can be considered as a realization of a lattice gas with a random internal field and random bonds. The predictions of this model are in good agreement with experimental phase diagrams and results of diffuse x-ray scattering from microscopic density fluctuations of hydrogen in ${\mathrm{Nb}}_{1-x}{\mathrm{Mo}}_x$ alloys.

We report successful operation of a neutron microscope using ultracold neutrons at the high-flux reactor at Grenoble. A sharp, achromatic image of an object slit was obtained at a magnification of 50. The measured resolution of 0.1 mm was limited mainly by the available beam intensity, not by aberrations.

A simple method is used to calculate the currents induced by static uniform electromagnetic fields in the ground state of a two-dimensional electron gas. This is done for both the relativistic and the nonrelativistic cases. This analysis is used to explain the apparent similarity between the anomalous vacuum current in three-dimensional quantum electrodynamics and the quantized Hall current. The different natures of the two currents are demonstrated, and it is shown that the effective action for the gauge field in the nonrelativistic case does not contain a genuine Chern-Simons term. This precludes any attempt to use the chiral anomaly to explain the quantized Hall effect.

Numerical studies of the dynamics of finite quantum spin chains are presented which show that quantum systems with few degrees of freedom ($N=7\mathrm{}$) can be described by equilibrium statistical mechanics. The success of the statistical description is seen to depend on the interplay between the initial state, the observable, and the Hamiltonian. This work clarifies the impact of integrability and conservation laws on statistical behavior. The relation to quantum chaos is also discussed.

The joint distribution of energy eigenvalues of a Hamiltonian is derived by means of the usual statistical laws of classical many-body systems. It makes a transition from the Poisson type to the Gaussian type depending on the value of a single parameter characteristic of the Hamiltonian.

It is shown that the criterion for smoothness of invariant tori in certain dissipative dynamical systems approaching chaos can be formulated in terms of an eigenvalue problem—a discrete Schrödinger equation in a potential generated by the map. By this method it is shown that there exists a continuous line through parameter space—the "critical line"—on which the invariant circles lose smoothness. It is explained why this line should approach smoothness for the very-high-order mode-locking regions and this corroborates earlier numerical results relating global scaling properties of dynamical systems to those of circle maps. Further, this method yields effective approximation schemes for obtaining the critical line.

Traditional WKB theory yields wave functions which have divergences and are not invariant under any reasonable class of transformations. This Letter presents alternative WKB wave functions which have no divergences and are symplectic invariants.

The use of nonunitary discrete, irreducible representations of Lie algebras is proposed as a method for the determination of widths and energies of resonances. The method is illustrated by explicit application to three kinds of resonances: in transmission over a well, in transmission over a barrier, and in barrier penetration for a family of one-dimensional potentials. The same procedure is also useful in an algebraic approach to scattering by a complex (optical) potential, and for parametrization of the resonant contribution to the scattering matrix.

It is shown that if the "standard quantum limit" is taken in a predictive sense, then a repeated measurement scheme involving contractive states, recently proposed by Yuen, does not break this limit.

Levinson's theorem relation phase shifts and bound states, developed for a short-range potential $V_{\mathrm{sh}}$, is extended to scattering by $V_{\mathrm{sh}}+V_{\mathrm{C}}$, where $V_{\mathrm{C}}$ is a repulsive Coulomb potential. The subtleties associated with $L=0\mathrm{}$, $E=0\mathrm{}$ bound states for $V_{\mathrm{sh}}$ alone are not present for $V_{\mathrm{sh}}+V_{\mathrm{C}}$. Information is also obtained on the relation between the nodal structure of the zero-incident-energy wave function and the number of bound states; some extensions to scattering by a compound target are possible.

The dynamics of an asymmetric double-well system coupled to a heat bath is studied at low temperatures where transitions between the wells involve quantum tunneling. The time evolution of the occupation probabilities of the wells is calculated by means of instanton techniques. For a wide range of parameters incoherent relaxation is found at a rate whose dependence both on temperature and bias is nonanalytic, in general.

We study quantum tunneling in a biased double-well potential in the presence of Ohmic dissipation with a friction coefficient $\alpha >1\mathrm{}$. The tunneling rate out of the metastable well is calculated in real time as a function of the temperature $T$ and bias energy $\epsilon$. The $T=0\mathrm{}$ result agrees with a droplet-model calculation in imaginary time. At low temperatures we find an enhancement to the $T=0\mathrm{}$ rate varying as ${\left(\frac{T}{\epsilon }\right)}^2$.

A study of intrinsic and noise-induced intermittency and low-frequency noise due to crises is reported for numerical simulations of the sinusoidally driven dampled pendulum and radiofrequency-driven Josephson junctions. The effects of fractal boundaries of the basins of attraction on the functional form, noise sensitivity, and noise scaling of low-frequency power spectra are considered.

Statistics of energy spectra are studied for quantum billiards, i.e., free motion of a particle in two dimensions surrounded by a hard wall. The transition from regular to irregular spectra observed in moments of nearest-neighbor spacing distributions for different shapes of the boundary is analyzed by a superposition of independent level sequences with Poisson and Wigner distributions. The rate of mixture of the two sequences is compared with the rate of phase volumes spanned by quasiperiodic and chaotic orbits of the corresponding classical motion.