We study the detailed out-of-equilibrium time evolution of a homogeneous Bose-Einstein condensate (BEC). We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the BEC. The interaction between fluctuations proves to be crucial in the mechanism of instability generation. We show the existence of two regimes in $k$ space, with a crossover for $k^2/2m\sim 2\lambda |{\varphi }_0{|}^2$, where $\lambda$ is the coupling constant and $|{\varphi }_0{|}^2$ is the condensate density. We deduce and solve a set of coupled equations that completely determines the nonequilibrium dynamics of the condensate density.

Impurity atoms propagating at variable velocities through a trapped Bose-Einstein condensate were produced using a stimulated Raman transition. The redistribution of momentum by collisions between the impurity atoms and the stationary condensate was observed in a time-of-flight analysis. The collisional cross section was dramatically reduced when the impurity velocity was reduced below the condensate speed of sound, in agreement with the Landau criterion for superfluidity. For large numbers of impurity atoms, we observed an enhancement of atomic collisions due to bosonic stimulation. This enhancement is analogous to optical super-radiance.

We consider a gas of attractively interacting cold fermionic atoms which are manipulated by laser light. The laser induces a transition from an internal state with large negative scattering length to one with almost no interactions. The process can be viewed as a tunneling of atomic population between the superconducting and the normal states of the gas. It can be used to detect the BCS ground state and to measure the superconducting order parameter.

We investigate the dynamics of a classical particle in a one-dimensional two-wave potential composed of two periodic potentials that are time independent and of the same amplitude and periodicity. One of the periodic potentials is externally driven and performs a translational motion with respect to the other. It is shown that, if one of the potentials is of the ratchet type, translation of the potential in a given direction leads to motion of the particle in the same direction, whereas translation in the opposite direction leaves the particle localized at its original location. Moreover, even if the translation is random, but still has a finite velocity, an efficient directed transport of the particle occurs.

The wavelength of the ${}^{57}\mathrm{Fe}$ Mössbauer radiation is measured with a relative uncertainty of 0.19 ppm by using almost exact Bragg backscattering from a reference silicon crystal. Its value is determined as ${\lambda }_{\mathrm{M}}=0.860\mathrm{}25474\left(16\right)\times {10}^{-10\mathrm{}}$ m. The corresponding Mössbauer photon energy is $E_{\mathrm{M}}=14\mathrm{}412.497\left(3\right)$ eV. The wavelength of the ${}^{57}\mathrm{Fe}$ Mössbauer radiation is easily reproducible with an accuracy of at least ${10}^{-11\mathrm{}}{\lambda }_{\mathrm{M}}$ and could be used as a length standard of atomic dimensions.

We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.

A pair of systems at different temperatures is a classic environment for a heat engine, which produces work during the relaxation to a common equilibrium. It is generally believed that a direct interaction between the two systems will always decrease the amount of the obtainable work, due to inevitable dissipation. Here a situation is reported where, in some time window, work can be gained due to the direct coupling, while dissipation is relevant only for much larger times. Thus, the amount of extracted work increases, at the cost of a change of the final state.

The quantal impulse cross section is derived in a novel form appropriate for direct classical correspondence. The classical impulse cross section is then uniquely defined and yields the first general classical expression for $n\ell {-n}^{\prime }{\ell }^{\prime }$ collisional transitions. The derived cross sections satisfy the optical theorem and detailed balance. Direct connection with the classical binary encounter approximation is also firmly established. The unified method introduced is general in its application to various collision and recombination processes and enables new directions of enquiry to be pursued quite succinctly.

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with ${\nu }_{\perp }=-\beta =1,{\nu }_{||}=\gamma /2=2$ (characteristic of short-range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents ${\nu }_{\perp }=-\beta =1\mathrm{}/2,{\nu }_{||}=\gamma /2=1$.

Based on the method of matched asymptotic expansions and on a time-dependent variational analysis, we study the dynamics of a vortex in a three-dimensional disk-shaped nonaxisymmetric condensate in the Thomas-Fermi limit. Both methods show that a vortex in a trapped Bose-Einstein condensate has formally unstable normal mode(s) with positive normalization and negative frequency, corresponding to a precession of the vortex line around the center of the trap. In a rotating trap, the solution becomes stable above an angular velocity ${\Omega }_m$, characterizing the onset of metastability with respect to small transverse displacements of the vortex from the central axis.

We present a new efficient method to find the Ising problem partition function for finite lattice graphs embeddable on an arbitrary orientable surface, with integral coupling constants bounded in the absolute value by a polynomial of the size of the lattice graph. The algorithm has been implemented for toroidal lattices using modular arithmetic and the generalized nested dissection method. The implementation has substantially better performance than any other as far as we know.

A novel WKB approach to calculating the lifetime of quasistationary states in the potential wells of the form $V\left(x\right)=P\left(x\right)-\mu Q\left(x\right)$, where $P\left(x\right)$ is the radial part of the potential for the spherically symmetric harmonic oscillator or the hydrogen atom and $Q\left(x\right)$ is a polynomial, is suggested. In this approach, the usual explicit procedure of the asymptotic matching of the perturbative and WKB wave functions is avoided and a simple formula for the imaginary part of the energy is found. The leading and the first correction terms for the imaginary part of the energy and the related lifetime are analytically calculated.

We show that particular configurations of intense off-resonant laser beams can give rise to an attractive $1/r$ interatomic potential between atoms located well within the laser wavelength. Such a “gravitational-like” interaction is shown to give stable Bose-Einstein condensates that are self-bound (without an additional trap) with unique scaling properties and measurably distinct signatures.

A mapping theorem leading to exact many-body dynamics of impenetrable bosons in one dimension reveals dark and gray solitonlike structures in a toroidal trap which is phase imprinted. On long time scales revivals appear that are beyond the usual mean-field theory.

We present two experiments testing the hypothesis of noncontextual hidden variables. The first one is based on observation of two-photon pseudo-Greenberger-Horne-Zeilinger correlations, with two of the originally three particles mimicked by the polarization degree of freedom and the spatial degree of freedom of a single photon. The second one, a single-photon experiment, utilizes the same trick to emulate two particle correlations, and is an “event ready” test of a Bell-like inequality, derived from the noncontextuality assumption. Modulo fair sampling, the data falsify noncontextual hidden variables.

Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.

We revisit the phenomenon of quantum stochastic resonance in the regime of validity of the Bloch equations. We find that a stochastic resonance behavior in the steady-state response of the system is present whenever the noise-induced relaxation dynamics can be characterized via a single relaxation time scale. The picture is validated by a simple nuclear magnetic resonance experiment on water.

Activated escape is investigated for systems that are driven by noise whose power spectrum peaks at a finite frequency. Analytic theory and analog and digital experiments show that the system dynamics during escape exhibit a symmetry-breaking transition as the width of the fluctuational spectral peak is varied. For double-well potentials, even a small asymmetry may result in a parametrically large difference of the activation energies for escape from different wells.

A Comment on the Letter by S. K. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by Astrid Lambrecht and Serve Renaud.