Novel vortex structures in dipolar condensates

We investigate the properties of single vortices and of vortex lattice in a rotating dipolar condensate. We show that vortices in this system possess many novel features induced by the long-range anisotropic dipolar interaction between particles. For example, when the dipoles are polarized along the rotation axis, vortices may display a crater-like structure; when dipoles are polarized orthogonal to the rotation axis, vortex cores takes an elliptical shape and the vortex lattice no longer possesses hexagonal symmetry.Comment: 4 pages, 5 figure

User's guide to four-body and three-body trajectory optimization programs

A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time

Phase space deformation of a trapped dipolar Fermi gas

We consider a system of quantum degenerate spin polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the Fermi gas in phase space and use it to examine the stability of the system. We emphasize the important roles played by the Fock exchange term of the dipolar interaction which results in a non-spherical Fermi surface.Comment: 5 pages, 5 figure

A consistent description of kinetic equation with triangle anomaly

We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for minimum number of unknown coefficients in one charge and two charge cases by solving the constraining equations.Comment: RevTex 4, 11 pages; With minor changes: typos are corrected and one reference is added. Accepted version to PR

Fermi liquid features of the one-dimensional Luttinger liquid

We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Fermi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the 1D Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the 1D Fermi-liquid and the Luttinger liquid.Comment: RevTeX, 5 pages, published versio

Making vortices in dipolar spinor condensates via rapid adiabatic passage

We propose to the create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can be qualitatively described by a simple rapid adiabatic passage model.Comment: 4 pages, 4 figure

Q -permutable subgroups of finite groups

A subgroup H of a group G is called Q-permutable in G if there exists a subgroup B of G such that (1) G=HB and (2) if H1 is a maximal subgroup of H containing HQG, then H1B=BH1<G, where HQG is the largest permutable subgroup of G contained in H. In this paper we prove that: Let F be a saturated formation containing U and G be a group with a normal subgroup H such that G/H∈F. If every maximal subgroup of every noncyclic Sylow subgroup of F∗(H) having no supersolvable supplement in G is Q-permutable in G, then G∈F.Пiдгрупу H групи G називають Q-переставною в G, якщо iснує пiдгрупа B групи G така, що: 1) G=HB та 2) якщо H1 — максимальна пiдгрупа H, що мiстить HQG, то H1B=BH1<G, де HQG є найбiльшою переставною пiдгрупою G, що мiститься в H. У цiй роботi доведено наступне твердження. Нехай F — насичена формацiя, що мiстить U, а G — група з нормальною пiдгрупою H такою, що G/H∈F. Якщо кожна максимальна пiдгрупа кожної нециклiчної силовської пiдгрупи F∗(H), що не має надрозв’язного доповнення в G, є Q-переставною в G, то G∈F

Does stability of relativistic dissipative fluid dynamics imply causality?

We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic dissipative fluid dynamics are always stable. We then perform a linear stability analysis in a Lorentz-boosted frame. Provided that the ratio of the relaxation time for the shear stress tensor, $\tau_\pi$, to the sound attenuation length, $\Gamma_s = 4\eta/3(\varepsilon+P)$, fulfills a certain asymptotic causality condition, the equations of motion give rise to stable solutions. Although the group velocity associated with perturbations may exceed the velocity of light in a certain finite range of wavenumbers, we demonstrate that this does not violate causality, as long as the asymptotic causality condition is fulfilled. Finally, we compute the characteristic velocities and show that they remain below the velocity of light if the ratio $\tau_\pi/\Gamma_s$ fulfills the asymptotic causality condition.Comment: 30 pages, 10 figures

Self-trapping of a Fermi super-fluid in a double-well potential in the BEC-unitarity crossover

We derive a generalized Gross-Pitaevskii density-functional equation appropriate to study the Bose-Einstein condensate (BEC) of dimers formed of singlet spin-half Fermi pairs in the BEC-unitarity crossover while the dimer-dimer scattering length $a$ changes from 0 to $\infty$. Using an effective one-dimensional form of this equation, we study the phenomenon of dynamical self-trapping of a cigar-shaped Fermi super-fluid in the entire BEC-unitarity crossover in a double-well potential. A simple two-mode model is constructed to provide analytical insights. We also discuss the consequence of our study on the self-trapping of an atomic BEC in a double-well potential.Comment: 10 pages, 9 figure