Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.     

Screening of magnetic fields by charged Bose condensate

The space-space component of the photon polarization operator is calculated in zero frequency limit for a medium with Bose-Einstein condensate (BEC) of electrically charged particles. It is found that the polarization operator tends to a finite value at vanishing photon 3-momentum, as it happens in superconducting media. It means that magnetic fields are exponentially screened in such a medium analogously to the Debye screening of electric charges. At non-zero temperature the screened magnetic field oscillates and contains a contribution which drops only as a power of distance. This phenomenon is unknown for superconductors, even in BEC phase and can be potentially observable.     

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.     

Bounds for a Bose condensate in dimensions v ⩾ 3

A stronger version of the Bogoliubov inequality is used to derive an upper bound for the anomalous average ¦x)>|s of an interacting nonrelativislic Bose fielda(x) at a finite temperature. This bound is ¦a(x)²|s <pR, whereR satisfies 1 -R = (RT/2T _c ^v/2, withv the dimensionality, andT _c the critical temperature in the absence of interactions. The formation of nonzero averages is closely related to the Bose-Einstein condensation and ¦|·² is often believed to coincide with the mean densitypa of the condensate. We have found nonrigorous arguments supporting the inequality po ? ¦|·², which parallels the result of Griffiths in the case of spin systems.     

Diffusion Monte Carlo analysis of the crossover from three to two dimensions for trapped Bose gases

We investigate the crossover from three to two dimensions for harmonically trapped hard-sphere Bose gases by varying the aspect ratio of the trapping potential. The diffusion Monte Carlo method is used to calculate both the ground-state energy and structural properties. The effect of trap anisotropy, interparticle interaction, and number of particles on the ground-state properties is discussed. Our results show that the minimum value of the aspect ratio at which the system reaches an asymptotic equilibrium distribution in the weakly confined direction decreases with increasing scattering length, while the minimum value of the aspect ratio at which the system enters the quasi-two-dimensional (2D) regime increases as both the scattering length and the number of particles increase. Additionally, the role played by particle correlations is proved to be more pronounced in the quasi-2D system than in the three-dimensional (3D) system by directly comparing the ground-state properties for the two cases.     

The disordered Bose condensate in two dimensions: application to high-Tc superconductors

We calculate the dynamical conductivity for a weakly disordered Bose condensate in two dimensions. The disorders is due to neutral impurities. We compare the asymptotic laws (for small and large frequencies) for neutral impurities with the ones for charged impurities. Universal functions for the dynamical transport properties are derived. The plasmon density of states shows a linear increase with energy for intermediate energies and a peak structure at larger energies. Our theoretical results are compared with experimental results (far-infrared, electron-energy-loss and Raman spectroscopy) found in the high-T_c superconductor YBa₂Cu₃O_7−δ. The occurrence of a quasi-gap in a disordered Bose condensate is described and discussed in connection with experiments on high-T_c superconductors.     

Bose condensate drag in a system of two coupled traps

A system of two plane traps disposed one above the other and confined atomic Bose condensate is considered. The possibility of entraining atoms of one of the traps by the atoms of the other trap upon the rotation of the latter is studied. The average angular momentum induced by the rotation of the first trap is found for the atoms in the second trap.     

Critical indices for the charged Bose gas

A self-consistent version of the static random phase approximation leads to a quasi-particle energy satisfying ?(k)=Ak^v for small k, where v ≈ 1.8. The critical indices are those of an ideal Bose gas with this spectrum.     

Spin correlations in electron liquids: Analytical results for the local-field correction in two and three dimensions

We study the spin correlations in two- and three-dimensional electron liquids within the sum-rule version of the self-consistent field approach of Singwi, Tosi, Land, and Sj?lander. Analytic expressions for the spin-antisymmetric static structure factor and the corresponding local-field correction are obtained with density dependent coefficients. We calculate the spin-dependent pair-correlation functions, paramagnon dispersion, and static spin-response function within the present model, and discuss the spin-density wave instabilities in double-layer electron systems. Received: 22 September 1997 / Revised: 1 December 1997 / Accepted: 4 December 1997     

Surprising results of soliton collisions in a three component Bose Einstein condensate

We investigate binary soliton collisions in three component BECs with spin exchange interactions and F = 1. For very special values of the coupling constants, these collisions are known to be elastic. We find that, for a further narrow range of parameters, collisions are almost elastic in the sense that a small amount of energy is lost in the process. Emergent solitons are almost identical to the original ones. However, the generic behaviour, found for most values of the two coupling constants, is very different. We observed the creation of spin component oscillations in both emerging entities. We therefore call these entities oscillatons. They are robust and fit an exact solution of the equations. Thus colliding two solitons can in general, somewhat unexpectedly, result in one of two very different outcomes.     

Evolution from BCS superconductivity to Bose condensation: analytic results for the crossover in three dimensions

We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution. Received: 9 May 1997 / Revised: 4 August 1997 / Accepted: 6 November 1997     

Scattering of neutrons on a Bose condensate

The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid ⁴He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.     

Spin orbit coupled Bose Einstein condensate in a two dimensional bichromatic optical lattice

We numerically investigate the localization of Bose Einstein condensate (BEC) with spin orbit coupling in a two dimensional bichromatic optical lattice. We study localization in weakly interacting and non-interacting regimes. The existence of stationary localized states in the presence of spin–orbit and Rabi couplings has been confirmed. We find that spin orbit coupling favors localization, whereas Rabi coupling has a slight delocalization effect.