A simple analytic expression for the ground state of a dilute gas of $N$ ideal bosons in a 3D harmonic potential at temperature $T$ is derived from the steady state solutions of nonequilibrium equations of motion. The $N$ particle constraint plays the important role of introducing the essential nonlinearity yielding a Ginzburg-Landau free energy. The present analysis has much in common with the quantum theory of the laser, and with the laser phase transition analogy.

In the effects of the Aharonov-Bohm type the topological properties of the phase shift are directly related to those of the linear and angular momentum of the electromagnetic fields. This interpretation leads to the formulation of a nonlocal topological effect for particles possessing an electric dipole moment. The experimental observation of this effect is within reach of atom or molecular interferometry.

A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$ matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known discrete and field models a new class of inhomogeneous and impurity models is obtained.

The harmonic measure (or diffusion field) near a critical percolation cluster in two dimensions (2D) is considered. Its moments, summed over the accessible external hull, exhibit a multifractal (MF) spectrum, which I calculate exactly. The generalized dimensions $D\left(n\right)$ as well as the MF function $f\left(\alpha \right)$ are derived from generalized conformal invariance, and are shown to be identical to those of the harmonic measure on 2D random or self-avoiding walks. An application to the impedance of a rough percolative electrode is given. The numerical checks are excellent.

A “persistence” exponent $\theta$ has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: For zero-temperature homogeneous Ising models on the $d$-dimensional cubic lattice $Z^d$, the fraction $p\left(t\right)$ of spins not flipped by time $t$ decays to zero like $t^{-\theta \left(d\right)}$ for low $d$; for high $d$, $p\left(t\right)$ may decay to $p\left(\infty \right)>0\mathrm{}$, because of “blocking” (but perhaps still like a power). What are the effects of disorder or changes of the lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low $d$, and then present two examples—one disordered and one homogeneous—where $p\left(t\right)$ decays exponentially to $p\left(\infty \right)$.

We show that the Casimir, or zero-point, energy of a dilute dielectric ball, or of a spherical bubble in a dielectric medium, coincides with the sum of the van der Waals energies between the molecules that make up the medium. That energy, which is finite and repulsive when self-energy and surface effects are removed, may be unambiguously calculated by either dimensional continuation or by zeta-function regularization. This physical interpretation of the Casimir energy seems to be unambiguous evidence that the bulk self-energy cannot be relevant to sonoluminescence.

We discuss how a consistent phase standard for Bose-Einstein condensates may be defined. We show that it has the properties we would wish for in a phase standard: it is not corrupted by subsequent comparisons. A quantum jump technique is employed to study the time evolution of a three mode condensate system on which we make measurements, which entangle the modes and so establish relative phases between them. By establishing, in turn, the phases of two condensates relative to a reference condensate, we show that the relative phase between them can be predicted accurately. The existence of such a phase standard gives a precise definition to the phase of a condensate.

In recently introduced schematic lattice gas models for vibrated dry granular media, we study the dynamical response of the system to small perturbations of shaking amplitudes and its relations with the characteristic fluctuations. Strong off equilibrium features, as negative responses, appear and a generalized version of the fluctuation dissipation theorem is introduced. The relations with thermal glassy systems and the role of Edwards' compactivity are discussed.

A Comment on the Letter by Seung-Yeon Kim and Richard J. Creswick, Phys. Rev. Lett. 81, 2000 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by James L. Monroe.

We introduce a fractional Fokker-Planck equation describing the stochastic evolution of a particle under the combined influence of an external, nonlinear force and a thermal heat bath. For the force-free case, a subdiffusive behavior is recovered. The equation is shown to obey generalized Einstein relations, and its stationary solution is the Boltzmann distribution. The relaxation of single modes is shown to follow a Mittag-Leffler decay. We discuss the example of a particle in a harmonic potential.

We have measured the absolute optical frequency of the cesium $D_1$ line at 335 THz (895 nm). This frequency provides an important link for a new determination of the fine structure constant $\alpha$. The $D_1$ line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at 88.4 THz ( $3.39\mu \mathrm{m}$). To measure the frequency mismatch of 18.39 THz between $4\times 88.4\mathrm{THz}=354\mathrm{}\mathrm{THz}$ and the $D_1$ line a frequency comb spanning around 244 000 modes of a Kerr-lens mode-locked laser was used. We find 1 167 688 (81) kHz for the hyperfine splitting of the ${6P}_{1/2}$ state and 335 116 048 807 (41) kHz for the hyperfine centroid from which we derive ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}9924\left(41\right)$.

We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index $q$ as a function of the Lévy index $\alpha$, and using dynamic rather than probabilistic arguments.

In this paper the dynamic behavior of an oscillating tip-microlever system at the proximity of a surface is discussed. We show that the nonlinear behavior of the oscillator is able to explain the high sensitivity of the oscillating tip microlever and the observed shifts of the resonance frequency as a function of the tip surface distance without the need of introducing a particular short range force.

We provide an explicit solution of the problem of activation escape from a metastable state of a periodically driven Brownian particle, including both the exponent and the prefactor. We find the instantaneous and time-average escape rates, and a crossover in their field dependence, from weak to exponentially strong, with amplitude and period of the driving field. The results apply for an arbitrary ratio between the field amplitude and the noise intensity, and between the field period and the relaxation time of the system.

This last of a series of three measurements improves the comparison of antiproton $\left(\overline{p}\right)$ and proton $\left(p\right)$ by almost a factor of ${10}^6$ over earlier exotic atom measurements, and is the most precise $\mathrm{CPT}$ test with baryons by a similar large factor. Measuring the cyclotron frequencies of a simultaneously trapped $\overline{p}$ and $H^{-}$ ion establishes that the ratio of $q/m$ for $\overline{p}$ and $p$ is $-0.999\mathrm{}99999991\pm 0.00000000009$, more than 10 times the accuracy over our previous measurement. This $9\times {10}^{-11\mathrm{}}$ comparison makes the first use of simultaneously trapped particles for sub-ppb spectroscopy.

A Comment on the Letter by S. Gao, Phys. Rev. Lett. 79, 3101 (1997). The authors of the Letter offer a Reply.

We investigate a novel stochastic technique for the global optimization of complex potential energy surfaces that avoids the freezing problem of simulated annealing by allowing the dynamical process to tunnel energetically inaccessible regions of the potential energy surfaces by way of a dynamically adjusted nonlinear transformation of the original potential energy surfaces. We demonstrate the success of this approach, which is characterized by a single adjustable parameter, for three generic hard minimization problems.

We demonstrate a continuous output coupler for magnetically trapped atoms. Over a period of up to 100 ms, a collimated and monoenergetic beam of atoms is continuously extracted from a Bose-Einstein condensate. The intensity and kinetic energy of the output beam of this atom laser are controlled by a weak rf field that induces spin flips between trapped and untrapped states. Furthermore, the output coupler is used to perform a spectroscopic measurement of the condensate, which reveals the spatial distribution of the magnetically trapped condensate and allows manipulation of the condensate on a micrometer scale.

We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of “noise” and “delay.” We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay.