We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices satisfy novel universal laws that only depend on a multicriticality of the bulk density of states near the soft edge of the spectrum. Our consideration is based on the previously unknown observation that the genuine density of states and the $n$-point correlation function are completely determined by the Dyson's density analytically continued onto the entire real axis.

We analyze the response of condensed trapped atoms to external driving magnetic fields. Solving the time-dependent Gross-Pitaewskii equation within a new, accurate algorithm, we found frequencies and relaxation times of collective oscillations in excellent agreement with the experimental results. Using simple scaling arguments we make quantitative predictions for future experiments.

We present the first theoretical treatment that accounts in detail for a recent observation of overlapping Bose-Einstein condensates of two different ${}^{87}\mathrm{Rb}$ hyperfine states [C. J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997)]. Despite the complicated geometry, we have completed a three-dimensional Hartree-Fock calculation for the coupled condensates. The calculation explains a number of its key properties: (i) The manner in which one condensate partially wraps around the other, (ii) the mean separation between the two condensates including the effects of gravity and of their mutual interaction, and (iii) the surprisingly long lifetime of the trap.

The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of nonequilibrium physics and the approach to equilibrium without the need for solving the nonlinear microscopic equations of motion or computing the time dependence of the probability distribution explicitly.

The effect of the rotation of the Earth, ${\Omega }_{\oplus }$, on a superfluid resonator equipped with a $4.0{\mathrm{cm}}^2$ rotation pickup loop and with a microaperture is reported. The velocity circulation induced in the loop by the rotation is detected by phase-slippage techniques. The magnitude of ${\Omega }_{\oplus }$ is measured to better than 1%, and the north direction to $\pm 0.5°$ for a 10 h observation time. This experiment is the superfluid counterpart of interferometric measurements based on the Sagnac effect.

A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency–wave-vector plane. For a single corrugated plate we find a correction to mass at low frequencies, and an effective shear viscosity at high frequencies, both anisotropic. For two plates there is resonant dissipation for all frequencies greater than the lowest optical mode of the cavity.

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings.

The quantum statistical mechanics of an ideal gas with fractional exclusion (i.e., Haldane-Wu) statistics in arbitrary dimensions is discussed. The general formulation for pressure and density of the system is obtained in a closed form in terms of the $D$-dimensional momentum representation, which can be regarded as a natural generalization of the classic results for Fermi and Bose gases. Using this, it is shown that ideal gases with fractional exclusion statistics can be regarded as composites of fermions and bosons, and that no condensation occurs at low temperature except for the pure boson case.

We have proposed a cluster heat bath method in Monte Carlo simulations of Ising models in which one of the possible spin configurations of a cluster is selected in accordance with its Boltzmann weight. We have argued that the method improves slow relaxation in complex systems and demonstrated it in an axial next-nearest-neighbor Ising model in two dimensions.

An upper bound for the coefficient of performance (COP) of endoreversible refrigerators which depends only on the ratio $\tau {=T}_c/T_h$ between the cold and hot reservoir temperatures has been elusive to date. We address here this long standing problem by analyzing an endoreversible Carnot refrigerator that operates in conditions of maximum per-unit-time COP. Two novel results are obtained: (1) A long sought $\tau$-dependent upper bound for the COP of refrigerators. (2) A $\tau$-dependent optimum distribution of the heat conductances associated with the coupling between the refrigerant and the heat reservoirs. Moreover, when the method is applied to heat engines, the resulting optimum efficiency is even closer to real efficiencies than the well-known Curzon-Ahlborn result.

$q$-derivatives can be identified with the generators of fractal and multifractal sets with discrete dilatation symmetries. Besides providing a natural language in which to discuss homogeneous functions with oscillatory amplitudes, this also allows one to discuss cascade models with continuous scale changes.

When a single particle from two independent entangled pairs is detected in a manner such that it is impossible to determine from which pair the single particle came, the remaining three particles become entangled in a GHZ state. This procedure can be realized with existing sources of entangled photons and with future sources of entangled atoms.

The issue of quantum barrier crossing and reflection in the time domain is addressed. We find that (1) classically forbidden barrier tunneling and above-barrier reflection are well-defined and important processes in the time domain, (2) classically forbidden processes can overshadow allowed ones when both are present, and (3) classically allowed trajectories in the time domain are not, in general, sufficient to explain tunneling amplitudes in the energy domain. We also make clear the essential distinction of barriers which flatten out at large distance and those which do not.

We study driven lattice gas systems with quenched spatial randomness: the disordered drop-push process, for which the steady state is shown to have inhomogeneous product measure form, and the disordered asymmetric exclusion process. We conjecture that time-dependent correlation functions which monitor dissipation of kinematic waves behave as in the pure system if the wave speed is nonzero, and support this with simulations. This speed vanishes close to half filling in the disordered exclusion process where macroscopic regions with different densities coexist.

This Letter presents an algorithm to obtain all local conservation laws for any system of field equations. The algorithm uses a formula which directly generates the conservation laws and does not depend on the system having a Lagrangian formulation, in contrast to Noether's theorem which requires a Lagrangian. Several examples are considered including dissipative systems inherently having no Lagrangian.

In the consistent histories formulation of quantum theory, the probabilistic predictions and retrodictions made from observed data depend on the choice of a consistent set. We show that this freedom allows the formalism to retrodict contrary propositions which correspond to orthogonal commuting projections and which each have probability one. We also show that the formalism makes contrary probability one predictions when applied to Gell-Mann and Hartle's generalized time-neutral quantum mechanics.

We try to clarify what are the genuine quantal effects that are associated with generalized Brownian motion. All the quantal effects that are associated with the Zwanzig-Feynman-Vernon-Caldeira-Leggett model are (formally) a solution of the classical Langevin equation. Nonstochastic, genuine quantum mechanical effects are found for a model that takes into account either the disordered or the chaotic nature of some environment.

We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic signals may be enhanced at multiple values of the noise level, instead of at a single value which has occurred in systems considered up to now in the framework of stochastic resonance.

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well-known exponents of Reggeon field theory. In addition, this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.