Slow 4He^{4}He Quenches Produce Fuzzy, Transient Vortices

We examine the Zurek scenario for the production of vortices in quenches of liquid $^{4}He$ in the light of recent experiments. Extending our previous results to later times, we argue that short wavelength thermal fluctuations make vortices poorly defined until after the transition has occurred. Further, if and when vortices appear, it is plausible that that they will decay faster than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title, this paper differs from its predecessor by including temperature, as well as pressure, quenche

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

Do attractive bosons condense?

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. ^7Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a `fragmented' condensate discussed by Nozi\`eres and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.Comment: 4 pages, Latex, RevTe

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive case. Our solutions take the form of bounded, quantized, stationary trains of bright solitons. Among them are two uniquely nonlinear classes of nodeless solutions, whose properties and physical meaning are discussed in detail. The full set of symmetry-breaking stationary states are described by the $C_{n}$ character tables from the theory of point groups. We make experimental predictions for the Bose-Einstein condensate and show that, though these are the analog of some of the simplest problems in linear quantum mechanics, nonlinearity introduces new and surprising phenomena.Comment: 11 pages, 9 figures -- revised versio

Fate of a Bose-Einstein condensate with attractive interaction

We calculate the decay amplitude of a harmonically trapped Bose-Einstein condensate with attractive interaction via the Feynman path integral. We find that when the number of particles is less than a critical number, the condensate decays relatively slowly through quantum tunneling. When the number exceeds the critical one, a "black hole" opens up at the center of the trap, in which density fluctuations become large due to a negative pressure, and collisional loss will drain the particles from the trap. As the black hole is fed by tunneling particles, we have a novel system in which quantum tunneling serves as a hydrodynamic source.Comment: 3 pages, REVTeX; email to [email protected] (Kerson Huang

Non-Ground-State Bose-Einstein Condensates of Trapped Atoms

The possibility of creating a Bose condensate of trapped atoms in a non-ground state is suggested. Such a nonequilibrium Bose condensate can be formed if one, first, obtains the conventional Bose condensate in the ground state and then transfers the condensed atoms to a non-ground state by means of a resonance pumping. The properties of ground and non-ground states are compared and plausible applications of such nonequilibrium condensates are discussed.Comment: 1 file, 16 pages, RevTe

Testing the Kibble-Zurek Scenario with Annular Josephson Tunnel Junctions

In parallel with Kibble's description of the onset of phase transitions in the early universe, Zurek has provided a simple picture for the onset of phase transitions in condensed matter systems, strongly supported by agreement with experiments in He3. In this letter we show how experiments with annular Josephson tunnel Junctions can and do provide further support for this scenario.Comment: Revised version with correct formula for the Swihart velocity. The results are qualitatively the same as with the previous version but differ quantitatively. 4 pages, RevTe

Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases

In this paper we use microscopic arguments to derive a nonlinear Schr\"{o}dinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the occupation of excited (bare particle) states affects the collisions, and thus obtain the many-body T-matrix approximation in a trap. In addition, we discuss how the bare particle many-body T-matrix gets dressed by mean fields due to condensed and excited atoms. We conclude that the most commonly used version of the Gross-Pitaevskii equation can only be put on a microscopic basis for a restrictive range of conditions. For partial condensation, we need to take account of interactions between condensed and excited atoms, which, in a consistent formulation, should also be expressed in terms of the many-body T-matrix. This can be achieved by considering fluctuations around the condensate mean field beyond those included in the conventional finite temperature mean field, i.e. Hartree-Fock-Bogoliubov (HFB), theory.Comment: Resolved some problems with printing of figure

Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials

We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii equation within the semi-classical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for finite number of particles at low temperature indicating a phase transition for weakly interacting systems.Comment: LaTeX, 6 pages, 8 figures, uses grafik.sty (included), to be published in Phys. Rev.