We study a system of hard-core particles sliding locally downwards on a fluctuating one-dimensional surface characterized by a dynamical exponent $z$ and no overall tilt. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale $\sim t^{1/z}$. The structure factor deviates from the Porod law for the models studied. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provide insight into this behavior.

The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main ideas by using a simple multibaker model, with some nonequilibrium initial state, and we study its progress toward equilibrium. The central results are (i) the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space, (ii) the rate of entropy production is largely independent of the scale of resolution used in the partitions, and (iii) the rate of entropy production is in agreement with the predictions of nonequilibrium thermodynamics.

Using homodyning with weak coherent fields and photon counting, we have observed violations of Bell-type inequalities by the generalized Einstein-Podolsky-Rosen state produced in a pulsed nondegenerate optical parametric amplifier, as predicted by Grangier et al. [Phys. Rev. A 38, 3132 (1988)]. The maximum observed visibility of the interference pattern was $(89\pm 4)\%$. This interference can be regarded as a manifestation of nonlocality in the sense described by Banaszek and Wodkiewicz [Phys. Rev. A 58, 4345 (1998)]. We have investigated the interference both theoretically and experimentally and have measured the influence of dispersion and phase matching.

A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic dipoles are obtained. Several new experiments are proposed, which include observation of topological phase shifts.

The pattern of activated trajectories in a symmetric double well system without detailed balance may contain cusps and other singularities, similar to the caustics of geometrical optics. We derive a scaling law and nonpolynomial “equations of state” that govern the bifurcation of an anomalous cusp (a cusp coinciding with the saddle) into conventional cusps. The bifurcation is reflected in the system quasipotential, much as a phase transition is reflected in the free energy of a thermodynamic system. The anomalous cusp is analogous to a nonclassical critical point. Besides showing how critical phenomena occur in noise-perturbed systems, our results extend classical catastrophe theory.

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions $d\le 2$, and we propose the appropriate low-dimensional modifications, which have a universal form. For $d=1\mathrm{}$ we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.

A Comment on the Letter by Hiromi Ezaki, Phys. Rev. Lett. 83, 3558 (1999). The authors of the Letter offer a Reply.

A Reply to the Comment by Morad Alexanian and Subir K. Bose.

A Comment on the Letter by Raffaele Resta, Phys. Rev. Lett. 80, 1800 (1998).

We systematically extend semiclassical real-time propagation methods based on Gaussian wave packets by using the composition property of the time-dependent quantum-mechanical Green function. For the first time, in an application to the problem of barrier tunneling, a semiclassical time-domain calculation of the transmission probability exhibits good agreement with exact quantum mechanical values at energies below the barrier top. Only two insertions of unity are needed for these results in a benchmark model of reactive scattering.

An effective field theory for the three-body system with large scattering length is applied to three-body recombination to a weakly bound $s$-wave state in a Bose gas. Our model independent analysis demonstrates that the three-body recombination constant $\alpha$ is not universal, but can take any value between zero and $67.9ħa^4/m$, where $a$ is the scattering length. Other low-energy three-body observables can be predicted in terms of $a$ and $\alpha$. Near a Feshbach resonance, $\alpha$ should oscillate between those limits as the magnetic field $B$ approaches the point where $a\to \infty$. In any interval of $B$ over which $a$ increases by a factor of 22.7, $\alpha$ should have a zero.

Stable numerical convolution of the diffusion impulse time response with a Gaussian wave packet produces a wave packet whose delay time is governed by an eikonal equation where the diffusivity distribution plays the role of the square of the velocity distribution. Diffusion delay time tomography data can approximately image the diffusivity distribution by solving an inverse problem for the eikonal equation with multiple rays that traverse low diffusivity regions not traversed by earlier related methods, and consequently the resolution in such regions is improved. This is important for medical imaging.

We study the robustness, against the leakage of bosons, of wave functions of interacting many bosons confined in a finite box by deriving and analyzing a general equation of motion for the reduced density operator. We identify a robust wave function that remains a pure state, whereas other wave functions, such as the Bogoliubov's ground state and the ground state with a fixed number of bosons, evolve into mixed states. Although these states all have the off-diagonal long-range order, and the same energy, we argue that only the robust state is realized as a macroscopic quantum state.

We report the observation of harmonic generation and strong nonlinear coupling of two collective modes of a condensed gas of rubidium atoms. Using a modified time averaged orbiting potential trap we changed the trap anisotropy to a value where the frequency of the $m=0\mathrm{}$ high-lying mode corresponds to twice the frequency of the $m=0\mathrm{}$ low-lying mode, thus leading to strong nonlinear coupling between these modes. By changing the anisotropy of the trap and exciting the low-lying mode we observed significant frequency shifts of this fundamental mode and also the generation of its second harmonic.

Yang and Yang proved that the divergence of $C_V\left(T\right)$ at a gas-liquid critical point implies that either $d^2{p/dT}^2\equiv p_{\sigma }^{\prime \prime }$ or $d^2\mu {/dT}^2\equiv {\mu }_{\sigma }^{\prime \prime }$ or both diverge when $T\to T_c-$ on the phase boundary $\sigma$. They queried the lattice-gas prediction that ${\mu }_{\sigma }^{\prime \prime }$ remains finite. Analysis of two-phase heat-capacity data provides, for the first time, evidence for such a Yang-Yang anomaly $({\mu }_{\sigma }^{\prime \prime }\to \pm \infty )$ in propane and suggests an anomaly of opposite sign in $\mathrm{CO}{}_2$. A revision of standard scaling theory for fluid criticality is demanded: specifically, ${p-p}_c$ must appear in the ordering field. The coexistence diameter hence gains a $|{T-T}_c{|}^{2\beta }$ term.

A Comment on the Letter by P.-A. Bares and M. Mobilia, Phys. Rev. Lett. 83, 5214 (1999). The authors of the Letter offer a Reply.

A Reply to the Comment by Su-Chan Park, Jeong-Man Park, and Doochul Kim.

A Comment on the Letter by Courtney L. Lopreore and Robert E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999). The authors of the Letter offer a Reply.

A Reply to the Comment by Jordi Sune and Xavier Oriols.