arXiv subjects

A. Griffin

Publications and source records attributed to A. Griffin.

36 records · Page 2Linked to original sources

arXiv2001

Dynamical instability of a condensate induced by a rotating thermal gas

We study surface modes of the condensate in the presence of a rotating thermal cloud in an axisymmetric trap. By considering collisions that transfer atoms between the condensate and noncondensate, we find that modes which rotate in the same sense as the thermal cloud damp less strongly than counter-rotating modes. We show that above a critical angular rotation frequency, equivalent to the Landau stability criterion, the co-rotating mode becomes dynamically unstable, leading to the possibility of vortex nucleation. This kind of mechanism is proposed as a natural explanation for the formation of vortices observed recently in the experiment of Haljan \emph{et al} {[}P. C. Haljan \emph{et al.}, cond-mat/0106362{]}. We also generalize our stability analysis to treat the case where the stationary state of the condensate already possesses a single vortex.

cond-mat↗

arXiv2000

Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud

We calculate the damping of condensate collective excitations at finite temperatures arising from the lack of equilibrium between the condensate and thermal atoms. We neglect the non-condensate dynamics by fixing the thermal cloud in static equilibrium. We derive a set of generalized Bogoliubov equations for finite temperatures that contain an explicit damping term due to collisional exchange of atoms between the two components. We have numerically solved these Bogoliubov equations to obtain the temperature dependence of the damping of the condensate modes in a harmonic trap. We compare these results with our recent work based on the Thomas-Fermi approximation.

cond-mat↗

arXiv2000

Quasiparticle kinetic equation in a trapped Bose gas at low temperatures

Recently the authors used the Kadanoff-Baym non-equilibrium Green's function formalism to derive kinetic equation for the non-condensate atoms, in conjunction with a consistent generalization of the Gross-Pitaevskii equation for the Bose condensate wavefunction. This work was limited to high temperatures, where the excited atoms could be described by a Hartree-Fock particle-like spectrum. We present the generalization of this recent work to low temperatures, where the single-particle spectrum is now described by the Bogoliubov-Popov approximation. We derive a kinetic equation for the quasiparticle distribution function with collision integrals describing scattering between quasiparticles and the condensate atoms. From the general expression for the collision integral for the scattering between quasiparticle excitations, we find the quasiparticle distribution function corresponding to local equilibrium. This expression includes a quasiparticle chemical potential that controls the non-diffusive equilibrium between condensate atoms and the quasiparticle excitations. We also derive a generalized Gross-Pitaevskii equation for the condensate wavefunction that includes the damping effects due to collisions between atoms in the condensate and the thermally excited quasiparticles. For a uniform Bose gas, our kinetic equation for the thermally excited quasiparticles reduces to that found by Eckern as well as Kirkpatrick and Dorfman.

cond-mat↗

arXiv2000

Damping of condensate collective modes due to equilibration with the non-condensate

We consider the damping of condensate collective modes at finite temperatures arising from lack of equilibrium between the condensate and the non-condensate atoms, an effect that is ignored in the usual discussion of the collisionless region. As a first approximation, we ignore the dynamics of the thermal cloud. Our calculations should be applicable to collective modes of the condensate which are oscillating out-of-phase with the thermal cloud. We obtain a generalized Stringari equation of motion for the condensate at finite temperatures, which includes a damping term associated with the fact that the condensate is not in diffusive equilibrium with the static thermal cloud. This inter-component collisional damping of the condensate modes is comparable in magnitude to the Landau damping considered in the recent literature.

cond-mat↗

arXiv1999

Two-fluid hydrodynamics of a Bose gas including damping from normal fluid transport coefficients

We extend our recent work on the two-fluid hydrodynamics of the condensate and non-condensate in a trapped Bose gas by including the dissipation associated with viscosity and thermal conduction. For purposes of illustration, we consider the hydrodynamic modes in the case of a uniform Bose gas. A finite thermal conductivity and shear viscosity give rise to a damping of the first and second sound modes in addition to that found previously due to the lack of diffusive equilibrium between the condensate and non-condensate. The relaxational mode associated with this equilibration process is strongly coupled to thermal fluctuations and reduces to the usual thermal diffusion mode above the Bose-Einstein transition. In contrast to the standard Landau two-fluid hydrodynamics, we predict a damped mode centered at zero frequency, in addition to the usual second sound doublet.

cond-mat.stat-mech↗

arXiv1999

Dynamics of trapped Bose gases at finite temperatures

Starting from an approximate microscopic model of a trapped Bose-condensed gas at finite temperatures, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. The kinetic equation includes collisions between the condensate and non-condensate atoms ($C_{12}$), in addition to collisions between the excited atoms as described by the Uehling-Uhlenbeck ($C_{22}$) collision integral. Assuming that the $C_{22}$ collision rate is sufficiently rapid to produce a local equilibrium Bose distribution, the kinetic equation can be used to derive hydrodynamic equations for the non-condensate. These equations include a description of the equilibration of the local chemical potentials of the condensate and non-condensate components which gives rise to a new relaxational mode associated with the exchange of atoms between the two components. We show how the Landau two-fluid equations emerge in the frequency domain $ωτ_μ\ll 1$, where $τ_μ$ is a characteristic relaxation time of the equilibration process. This process provides an additional source of damping of the collective modes (first and second sound in the case of a uniform system). Our equations are consistent with the generalized Kohn theorem. Finally, a variational solution of the equations is developed which is used to determine some of the monopole, dipole and quadrupole normal modes of a trapped Bose gas in an isotropic trap.

cond-mat.stat-mech↗

arXiv1999

Two-fluid dynamics for a Bose-Einstein condensate out of local equilibrium with the non-condensate

We extend our recent work on the two-fluid hydrodynamics of a Bose-condensed gas by including collisions involving both condensate and non-condensate atoms. These collisions are essential for establishing a state of local thermodynamic equilibrium between the condensate and non-condensate. Our theory is more general than the usual Landau two-fluid theory, to which it reduces in the appropriate limit, in that it allows one to describe situations in which a state of complete local equilibrium between the two components has not been reached. The exchange of atoms between the condensate and non-condensate is associated with a new relaxational mode of the gas.

cond-mat↗

arXiv1998

Hydrodynamic modes and pulse propagation in a cylindrical Bose gas above the Bose-Einstein transition

We study hydrodynamic oscillations of a cylindrical Bose gas above the Bose-Einstein transition temperature using the hydrodynamic equations derived by Griffin, Wu and Stringari. This extends recent studies of a cylindrical Bose-condensed gas at T=0. Explicit normal mode solutions are obtained for non-propagating solutions. In the classical limit, the sound velocity is shown to be the same as a uniform classical gas. We use a variational formulation of the hydrodynamic equations to discuss the propagating modes in the degenerate Bose-gas limit and show there is little difference from the classical results.

cond-mat↗

arXiv1998

Hydrodynamic damping in trapped Bose gases

Griffin, Wu and Stringari have derived the hydrodynamic equations of a trapped dilute Bose gas above the Bose-Einstein transition temperature. We give the extension which includes hydrodynamic damping, following the classic work of Uehling and Uhlenbeck based on the Chapman-Enskog procedure. Our final result is a closed equation for the velocity fluctuations $δv$ which includes the hydrodynamic damping due to the shear viscosity $η$ and the thermal conductivity $κ$. Following Kavoulakis, Pethick and Smith, we introduce a spatial cutoff in our linearized equations when the density is so low that the hydrodynamic description breaks down. Explicit expressions are given for $η$ and $κ$, which are position-dependent through dependence on the local fugacity when one includes the effect of quantum degeneracy of the trapped gas. We also discuss a trapped Bose-condensed gas, generalizing the work of Zaremba, Griffin and Nikuni to include hydrodynamic damping due to the (non-condensate) normal fluid.

cond-mat↗

arXiv1997

First and second sound in a uniform Bose gas

We have recently derived two-fluid hydrodynamic equations for a trapped weakly-interacting Bose gas. In this paper, we use these equations to discuss first and second sound in a uniform Bose gas. These results are shown to agree with the predictions of the usual two-fluid equations of Landau when the thermodynamic functions are evaluated for a weakly-interacting gas. In a uniform gas, second sound mainly corresponds to an oscillation of the superfluid (the condensate) and is the low frequency continuation of the Goldstone-Bogoliubov symmetry-breaking mode.

cond-mat↗

arXiv1997

Two-Fluid Hydrodynamics for a Trapped Weakly-Interacting Bose Gas

We derive the coupled equations of motion for the condensate (superfluid) and non-condensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wavefunction and an assumption of local equilibrium for the non-condensate atoms. In the case of a uniform weakly-interacting gas, our formalism gives a microscopic derivation of the well-known two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analogue of the out-of-phase second sound mode in uniform systems.

cond-mat↗

arXiv1996

Finite temperature excitations of a trapped Bose gas

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantitites are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a realtively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting gas in the high temperature limit.

cond-mat↗

arXiv1996

Hydrodynamic modes in a trapped Bose gas above the Bose-Einstein transition

We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at $T=0$ within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the $m=0$ excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.

cond-mat↗

arXiv1996

Quantized hydrodynamic model and the dynamic structure factor for a trapped Bose gas

We quantize the recent hydrodynamic analysis of Stringari for the low-energy collective modes of a trapped Bose gas at $T=0$. This is based on the time-dependent Gross-Pitaevskii equation, but omits the kinetic energy of the density fluctuations. We diagonalize the hydrodynamic Hamiltonian in terms of the normal modes associated with the amplitude and phase of the inhomogeneous Bose order parameter. These normal modes provide a convenient basis for calculating observable quantities. As applications, we calculate the depletion of the condensate at $T=0$ as well as the inelastic light-scattering cross section $S({\bf q},ω)$ from low-energy condensate fluctuations. The latter involves a sum over all normal modes, with a weight proportional to the square of the ${\bf q}$ Fourier component of the density fluctuation associated with a given mode. Finally, we show how the Thomas-Fermi hydrodynamic description can be derived starting from the coupled Bogoliubov equations.

cond-mat↗

arXiv1996

The Surface Region of Superfluid $^4$He as a Dilute Bose-Condensed Gas

In the low-density surface region of superfluid $^4$He, the atoms are far apart and collisions can be ignored. The only effect of the interactions is from the long-range attractive Hartree potential produced by the distant high-density bulk liquid. As a result, at $T=0$, all the atoms occupy the same single-particle state in the low-density tail. Striking numerical evidence for this 100\% surface BEC was given by Pandharipande and coworkers in 1988. We derive a generalized Gross-Pitaevskii equation for the inhomogeneous condensate wave function $Φ(z)$ in the low-density region valid at all temperatures. The overall amplitude of $Φ(z)$ is fixed by the bulk liquid, which ensures that it vanishes everywhere at the bulk transition temperature.

cond-mat↗

arXiv1996

Surface Contribution to Raman Scattering from Layered Superconductors

Generalizing recent work, the Raman scattering intensity from a semi-infinite superconducting superlattice is calculated taking into account the surface contribution to the density response functions. Our work makes use of the formalism of Jain and Allen developed for normal superlattices. The surface contributions are shown to strongly modify the bulk contribution to the Raman-spectrum line shape below $2Δ$, and also may give rise to additional surface plasmon modes above $2Δ$. The interplay between the bulk and surface contribution is strongly dependent on the momentum transfer $q_\parallel$ parallel to layers. However, we argue that the scattering cross-section for the out-of-phase phase modes (which arise from interlayer Cooper pair tunneling) will not be affected and thus should be the only structure exhibited in the Raman spectrum below $2Δ$ for relatively large $q_\parallel\sim 0.1Δ/v_F$. The intensity is small but perhaps observable.

cond-mat↗

arXiv1995

Surface Region of Superfluid Helium as an Inhomogeneous Bose-Condensed Gas

We present arguments that the low density surface region of self-bounded superfluid $^4$He systems is an inhomogeneous dilute Bose gas, with almost all of the atoms occupying the same single-particle state at $T = 0$. Numerical evidence for this complete Bose-Einstein condensation was first given by the many-body variational calculations of $^4$He droplets by Lewart, Pandharipande and Pieper in 1988. We show that the low density surface region can be treated rigorously using a generalized Gross-Pitaevskii equation for the Bose order parameter.

cond-mat↗

arXiv1995

Rigorous Density Functional Theory for Inhomogeneous Bose-Condensed Fluids

The density functional theory originally developed by Hohenberg, Kohn and Sham provides a rigorous conceptual framework for dealing with inhomogeneous interacting Fermi systems. We extend this approach to deal with inhomogeneous interacting Bose-condensed systems, limiting this presentation to setting up the formalism to deal with ground state $(T=0)$ properties. The key new feature is that one must deal with energy functionals of both the local density $n({\bf r})$ and the local complex macroscopic wavefunction $Φ({\bf r})$ associated with the Bose broken-symmetry (the local condensate density is $n_{c}({\bf r}) = \vert Φ({\bf r}) \vert ^{2}$). Implementing the Kohn-Sham scheme, we reduce the problem to a gas of weakly-interacting Bosons moving in self-consistent diagonal and off-diagonal one-body potentials. Our formalism should provide the basis for studies of the surface properties of liquid $^4$He as well as the properties of Bose-condensed atomic gases trapped in external potentials.

cond-mat↗