Thermodynamic inequalities in superfluid

We investigate general thermodynamic stability conditions for the superfluid. This analysis is performed in an extended space of thermodynamic variables containing (along with the usual thermodynamic coordinates such as pressure and temperature) superfluid velocity and momentum density. The stability conditions lead to thermodynamic inequalities which replace the Landau superfluidity criterion at finite temperatures.Comment: 7 pages, 1 figur

Infusing Problem-Based Learning (PBL) Into Science Methods Courses Across Virginia

This article outlines the results of a collaborative study of the effects of infusing problem-based learning (PBL) into K-12 science methods courses across four universities in Virginia. Changes in pre-service teachers\u27 attitudes surrounding science teaching were measured before and after completing a science methods course in which they experienced PBL first-hand as participants, and then practiced designing their own PBL units for use in their future classrooms. The results indicate that exposure to PBL enhances pre-service teachers\u27 knowledge of inquiry methods and self-efficacy in teaching science

Breathers on quantized superfluid vortices

We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings

Vortex signatures in annular Bose-Einstein condensates

We consider a Bose-Einstein condensate confined in a ``Mexican hat'' potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply-quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.Comment: 11 pages, 7 figure

Vibrations of a Columnar Vortex in a Trapped Bose-Einstein Condensate

We derive a governing equation for a Kelvin wave supported on a vortex line in a Bose-Einstein condensate, in a rotating cylindrically symmetric parabolic trap. From this solution the Kelvin wave dispersion relation is determined. In the limit of an oblate trap and in the absence of longitudinal trapping our results are consistent with previous work. We show that the derived Kelvin wave dispersion in the general case is in quantitative agreement with numerical calculations of the Bogoliubov spectrum and offer a significant improvement upon previous analytical work.Comment: 5 pages with 1 figur

Longitudinal and transverse forces on a vortex in superfluid 4^4He

We examine the transverse and longitudinal components of the drag force upon a straight vortex line due to the scattering of liquid $^4$He excitations. For this purpose, we consider a recently proposed Hamiltonian that describes the dissipative motion of a vortex, giving an explicit expression for the vortex-quasiparticle interaction. The involved dissipative coefficients are obtained in terms of the reservoir correlation function. Most of our explicit calculations are concerned to the range of temperatures below 0.4 K, at which the reservoir is composed by phonon quasiparticle excitations. We also discuss some important implications in the determination of possible scattering processes leading to dissipation, according to the values of vortex mass found in the literature.Comment: 10 pages, 2 figures, latex2e (iopart.cls), enlarged version submitted to J. Phys.: Condensed Matte

Vortex dynamics of rotating dipolar Bose-Einstein condensates

We study the influence of dipole-dipole interaction on the formation of vortices in a rotating dipolar Bose-Einstein condensate (BEC) of $^{52}$Cr and $^{164}$Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross-Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices while a repulsive contact interaction increases the stability of the vortices. Further, an ordered vortex lattice of relatively large number of vortices is found in a strongly dipolar BEC.Comment: 15 pages, 10 figures, 1 tabl

Inelastic electron-nucleus scattering and scaling at high inelasticity

Highly inelastic electron scattering is analyzed within the context of the unified relativistic approach previously considered in the case of quasielastic kinematics. Inelastic relativistic Fermi gas modeling that includes the complete inelastic spectrum - resonant, non-resonant and Deep Inelastic Scattering - is elaborated and compared with experimental data. A phenomenological extension of the model based on direct fits to data is also introduced. Within both models, cross sections and response functions are evaluated and binding energy effects are analyzed. Finally, an investigation of the second-kind scaling behavior is also presented.Comment: 39 pages, 13 figures; formalism extended and slightly reorganized, conclusions extended; to appear in Phys. Rev.

Critical frequency for vortex nucleation in Bose-Fermi mixtures in optical lattices

We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since 87Rb-40K mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system.Comment: 5 pages, 4 figures, revtex