We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of the wave packets which is anomalous for an interval of the characterizing power-law exponent. We also prove that the number of finite moments of the wave packets is a conserved quantity during the evolution of the wave packet in the free space.

The exact eigenspectra and eigenstates of spin-1 and spin-2 Bose-Einstein condensates (BECs) are found, and their response to a weak magnetic field is studied and compared with their mean-field counterparts. Whereas mean-field theory predicts the vanishing population of the zero magnetic-quantum-number component of a spin-1 antiferromagnetic BEC, the component is found to become populated as the magnetic field decreases. The spin-2 BEC exhibits an even richer magnetic response due to quantum correlations among three bosons.

We investigate the nucleation, annihilation, and dynamics of kinks in a classical $(1+1)-\mathrm{dimensional}$ ${\phi }^4$ field theory at finite temperature. From large scale Langevin simulations, we establish that the nucleation rate is proportional to the square of the equilibrium density of kinks. We identify two annihilation time scales: one due to kink-antikink pair recombination after nucleation, the other from nonrecombinant annihilation. We introduce a mesoscopic model of diffusing kinks based on “paired” and “survivor” kinks and antikinks. Analytical predictions for the dynamical time scales, as well as the corresponding length scales, are in good agreement with the simulations.

In this article we show that the three-particle Greenberger-Horne-Zeilinger theorem can be reformulated in terms of inequalities, allowing imperfect correlations due to detector inefficiencies. We show quantitatively that taking into account these inefficiencies, the published results of the Innsbruck experiment support the nonexistence of local hidden variables that explain the experimental results.

We derive a master equation for a mirror interacting with the vacuum field via radiation pressure. The dynamical Casimir effect leads to decoherence of a superposition state in a time scale that depends on the degree of “macroscopicity” of the state components, and which may be much shorter than the relaxation time scale. Coherent states are selected by the interaction as pointer states.

Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an unambiguous description of the quantal dynamics. This is shown explicitly for a single spin $s,$ using a quorum of expectation values which contains no redundant information. The quantum mechanical time evolution of the system is rephrased in terms of a closed set of linear first-order differential equation coupling $(2s+1{)}^2$ expectation values. This new representation of the dynamical law refers neither to the wave function of the system nor to its statistical operator.

Using a focused laser beam we stir a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ confined in a magnetic trap and observe the formation of a vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to four vortices are simultaneously present. We have also measured the lifetime of the single vortex state after turning off the stirring laser beam.

Surface modes in a Bose-Einstein condensate of sodium atoms have been studied. We observed excitations of standing and rotating quadrupolar and hexadecapolar modes. The modes were excited with high spatial and temporal resolution using the optical dipole force of a rapidly scanning laser beam. This novel technique is very flexible and should be useful for the study of rotating Bose-Einstein condensates and vortices.

To analyze phase transitions in a nonequilibrium system, we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can be identified with two different phases. In a region of the parameter space, both of these phases coexist. The condensation point can be computed with high accuracy.

The overdamped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model works as a detector for potential fluctuations being not too fast and not too slow. This effect occurs due to the different time scales in the problem. We present a detailed analysis of this effect using the exact solution of the Fokker-Planck equation for a simple model. Further we show that for not too fast fluctuations the system can be well described by effective rate equations. The results of the rate equations agree quantitatively with the exact results.

A moving dielectric medium acts as an effective gravitational field on light. One can use media with extremely low group velocities [Lene Vestergaard Hau et al., Nature (London) 397, 594 (1999)] to create dielectric analogs of astronomical effects on Earth. In particular, a vortex flow imprints a long-ranging topological effect on incident light and can behave like an optical black hole.

We propose to engineer the atomic band structure in optical lattices in order to design a Fabry-Perot interferometer with large mode spacing and strong nonlinear coupling to be employed in atom optics. The use of an optical lattice allows for a significant reduction of the atomic effective mass, while the slow modulation of its parameters spatially confines the matter waves on a length scale of a few dozen optical wavelengths. As a consequence, the mode spacing in such a cavity would be as high as one-tenth of the recoil energy, allowing for a very efficient filter action, while the nonlinear coupling due to interatomic interactions could lead to bistability and limiting effects in the transmission of the atomic beam.

Recent massive numerical simulations have shown that the response of a “stochastic resonator” is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using nonequilibrium potential techniques. We now consider a field-dependent diffusivity and show that the selectivity of the coupling is more efficient for achieving stochastic-resonance enhancement than its overall value in the constant-diffusivity case.

Driven diffusion of a Brownian particle along a one-dimensional lattice is investigated numerically on decreasing its damping constant. The notions of multiple jumps, jump reversal, and backward-to-forward rates are discussed in detail. In particular, we conclude that in the underdamped limit backward jumps are suppressed relative to forward jumps more effectively than previously assumed. The dependence of such a drive-controlled mechanism on the damping constant and the temperature is interpreted analytically.

We analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as $r^{-\alpha }$ where $r$ is the interparticle distance and $\alpha \ge 0$. By integrating the equations of motion we obtain the microcanonical time averages of both the magnetization and the kinetic energy. We detect three different regimes depending on whether $\alpha$ belongs to the intervals $[0,1)$, $(1,2)$, or $(2,\infty )$. For $0<\mathrm{}\alpha <1\mathrm{}$, the microcanonical averages agree, after a scaling, with those obtained in the canonical ensemble for the mean-field case $(\alpha =0\mathrm{})$. This correspondence offers a mathematically tractable way of dealing with systems governed by slowly decaying long-range interactions.

A Comment on the Letter by Mikhail Dzugutor, Erik Aurell, and Angelo Vulpiani, Phys. Rev. Lett. 81, 1762 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by E. G. D. Cohen and L. Rondoni.

We report a delayed “choice” quantum eraser experiment of the type proposed by Scully and Drühl (where the “choice” is made randomly by a photon at a beam splitter). The experimental results demonstrate the possibility of delayed determination of particlelike or wavelike behavior via quantum entanglement. The which-path or both-path information of a quantum can be marked or erased by its entangled twin even after the registration of the quantum.

A Comment on the Letter by D. Home and R. Chattopadhyaya, Phys. Rev. Lett. 76, 2836 (1996).

A Comment on the Letter by Stephen J. Cornell, Michael R. Swift, and Alan J. Bray, Phys. Rev. Lett. 81, 1142 (1998). The authors of the Letter offer a Reply.