A heuristic argument predicting the existence and critical temperature of a phase transition in the Coulomb gas in any dimensionality D>1 is advanced. Numerical simulations are reported, corroborating these predictions in two and three dimensions. They lead to an interpretation of the Kosterlitz-Thouless transition, different from the standard one, of dipole dissociation. In three dimensions, the transition is interpreted as the first-order liquid-gas one, across which the density is discontinuous.

We point out that the nondiffracting ${\mathrm{J}}_0$ beams of Durnin, Miceli, and Eberly are subgroup-reduced basis functions for the group of paraxial (symplectic, linear) transformations of optical phase space. This allows the action of the group on such and similar beams to be computed through 2×2 matrix algebra.

Examples of time-dependent kinematic magnetic dynamos arising from chaotic flows in the zero-resistivity limit are presented. These examples suggest that typically (1) the flux concentrates on a fractal, and (2) the magnetic field exhibits arbitrarily fine-scaled oscillations between parallel and antiparallel directions. Results quantitatively relating these effects to the dynamo growth rate are presented.

We have demonstrated 42% squeezing of 4.2-K thermal noise using a Josephson-parametric amplifier operated at 19.4 GHz. The amplifier has been operated at 0.1 K with an excess noise of 0.28 K referred to the input port. This is less than the vacuum fluctuation noise hν/2k=0.47 K at 19.4 GHz. The amplifier thus is less noise than a linear phase-insensitive amplifier such as a maser could in principle be.

The probability of tunneling of the magnetization in a single-domain particle through an energy barrier between easy directions is calculated for several forms of magnetic anisotropy. Estimated tunneling rates prove to be large enough for observation of the effect with the use of existing experimental techniques.

This Letter reexamines questions about the practicality of computing the exact stability domains of certain classes of pendulum systems. We display plots showing that the intertwining of neighboring domains have a self-affine truncated-fractal structure. A simple proof of the existence of diffeomorphisms from connected basins to striated basins is also presented.

Critical correlation in thermal systems, Ising spins for example, is approximately described by clusters. A cluster is defined as a randomly picked, connected region of excess up (or down) spins. Its simulation utilizes a branching-out stochastic chain which allots spins continuously, either to the cluster or to a perimeter of average composition. Results in dimensionality from 2 to 10 show the cluster geometry to be very different than in (athermal) percolation.

The coding of chaotic trajectories in Hamiltonian systems and the stochastic reflection of points on circles introduce examples of a new kind of multifractal measure, whose Hölder α ranges all the way from 0 to ∞.

Whenever the escaping entity and the thermal reservoir in contact with it move at comparable rates, escape must be viewed as due to diffusion in the space of the action variables. For almost integrable systems, the effective barrier height is argued to exceed substantially the potential-energy barrier of conventional theory, at least in the common case in which the potential barrier arises from terms in the Hamiltonian responsible for the nonintegrability, and to the extent that the usual quasiperturbative treatment of almost integrable systems is applicable at energies of order of the barrier.

We analyze the effect of irregular classical scattering on the corresponding quantum-mechanical scattering matrix. Using semiclassical arguments, we show that the fluctuations in the S matrix and the cross sections are consistent with a random-matrix description (Ericson fluctuations). The results are illustrated by a numerical solution of a simple quantum problem, whose classical counterpart displays irregular scattering.

We investigate the problem of inequivalent quantizations of a physical system with multiply connected configuration space X. For scalar quantum theory on X we show that state vectors must be single valued if and only if the first homology group ${\mathrm{H}}_1$(X) is trivial, or equivalently the fundamental group ${\mathrm{\pi }}_1$(X) is perfect. The θ structure of quantum gauge and gravitational theories is discussed in light of this result.

An explicit interaction-Hamiltonian realization of a measurement of the free-mass position with the following properties is given: (1) The probability distribution of the readouts is exactly the same as the free-mass position distribution just before the measurement. (2) The measurement leaves the free mass in a contractive state just after the measurement. It is shown that this measurement breaks the standard quantum limit for the free-mass position in the sense sharpened by the recent controversy.

We extend the inverse problem for multifractals to include the generalized logarithmic dimensions and the generalized metadimensions. These dimensions are shown to contribute characteristic $n$-dependent corrections to the scaling function, where $n$ is the stage of scaling refinement. We establish a connection between these corrections and the type of dimensions and demonstrate the utility of such a connection in the specific case of one-dimensional maps.

We report a new value for the universal gas constant $R:8.314471\mathrm{}\pm 0.000014$ J ${\mathrm{mol}}^{-1\mathrm{}}$ ${\mathrm{K}}^{-1\mathrm{}}$. The standard error of $R$ has been reduced by a factor of 5, to 1.7 ppm. $R$ was determined from the speed of sound in argon contained within a thick, spherical shell at the temperature of the triple point of water $T_t$. The volume of the shell was measured by our weighing the mercury required to fill it at $T_t$. The molar mass of the argon was determined relative to that of a standard with accurately known chemical and isotopic composition by use of speed-of-sound data.

The calculation of rapidly converging lower and upper bounds to the ground-state energy, $E_g$, of hydrogenic atoms in superstrong magnetic fields ($B\gtrsim {10}^9$ G) has been an important theoretical problem for the past twenty-five years. Much effort has gone into reconciling the many different estimates for $E_g$ predicted by an assortment of techniques. On the basis of recently developed eigenvalue moment methods, a precise solution involving rapidly converging bounds to $E_g$ for arbitrary superstrong magnetic field strengths, is now possible.

We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean which is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.

We have constructed a prototype transmission positron microscope (TPM) and taken magnified pictures of various objects with it. Information gained from the prototype TPM has allowed us to predict resolutions achievable in the near future with an upgraded TPM. Applications are discussed.

We consider a noncanonical ensemble which involves a sample thermally connected to a finite heat bath with specific properties. Treating the size of the heat bath as a parameter, we show that static properties of finite samples are ensemble dependent. Monte Carlo simulations of phase transitions in Potts models confirm the analysis and demonstrate significant reductions in computer time (sometimes by a factor of 100) compared to canonical-ensemble simulations. For finite samples, second-order transitions are sharpened and are clearly distinguished from first-order transitions as the heat bath becomes smaller.

We report on a novel experiment sensitive to the anisotropy of the one-way speed of light. The frequency of a two-photon transition in a fast atomic beam is compared to the frequency of a stationary absorber while the direction of the fast beam is rotated relative to the fixed stars. The experiment yields an improved upper limit for the anisotropy: $\frac{\Delta c}{c}\le 3\times {10}^{-9\mathrm{}}$.

The statistical properties of the quasienergy spectrum are used to measure the influence of quantum effects on the quantum kicked rotator which displays chaotic behavior in the classical limit. A transition from orthogonal-ensemble statistics in the semiclassical limit ($\hslash \to 0$) to Poisson statistics in the quantum regime is observed. In view of previously obtained results for this system the dependence on the irrationality of $\hslash$ is discussed.