Thermodynamic properties of a dipolar Fermi gas

Based on the semi-classical theory, we investigate the thermodynamic properties of a dipolar Fermi gas. Through a self-consistent procedure, we numerically obtain the phase space distribution function at finite temperature. We show that the deformations in both momentum and real space becomes smaller and smaller as one increases the temperature. For homogeneous case, we also calculate pressure, entropy, and heat capacity. In particular, at low temperature limit and in weak interaction regime, we obtain an analytic expression for the entropy, which agrees qualitatively with our numerical result. The stability of a trapped gas at finite temperature is also explored

BCS-BEC crossover and quantum phase transition for 6Li and 40K atoms across Feshbach resonance

We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold 6Li and 40K atoms across a wide Feshbach resonance. The background scattering lengths for 6Li and 40K have opposite signs, which lead to very different behaviors for these two types of atoms. For 40K, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For 6Li, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of 40K, there is a quantum phase transition at zero temperature from the superfluid to the normal fermi gas at the positive detuning of the magnetic field where the s-wave scattering length passes its zero point. For 6Li, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.Comment: 7 pages, 6 figure

Dynamical properties of a trapped dipolar Fermi gas at finite temperature

We investigate the dynamical properties of a trapped finite-temperature normal Fermi gas with dipole-dipole interaction. For the free expansion dynamics, we show that the expanded gas always becomes stretched along the direction of the dipole moment. In addition, we present the temperature and interaction dependences of the asymptotical aspect ratio. We further study the collapse dynamics of the system by suddenly increasing the dipolar interaction strength. We show that, in contrast to the anisotropic collapse of a dipolar Bose-Einstein condensate, a dipolar Fermi gas always collapses isotropically when the system becomes globally unstable. We also explore the interaction and temperature dependences for the frequencies of the low-lying collective excitations.Comment: 11 pages, 7 figure

Phase diagram of a polarized Fermi gas across a Feshbach resonance in a potential trap

We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions.Comment: 9 pages, 4 figure

Suppression of ferromagnetic ordering in doped manganites: Effects of the superexchange interaction

From a Monte Carlo study of the ferromagnetic Kondo lattice model for doped manganites, including the antiferromagnetic superexchange interaction ($J_{AF}$), we found that the ferromagnetic ordering was suppressed as $J_{AF}$ increased. The ferromagnetic transition temperature $T_c$, as obtained from a mean field fit to the calculated susceptibilities, was found to decrease monotonically with increasing $J_{AF}$. Further, the suppression in $T_c$ scales with the bandwidth narrowing induced by the antiferromagnetic frustration originating from $J_{AF}$. From these results, we propose that the change in the superexchange interaction strength between the $t_{2g}$ electrons of the Mn ions is one of the mechanisms responsible for the suppression in $T_c$ observed in manganites of the type (La$_{0.7-y}$Pr$_{y}$)Ca$_{0.3}$MnO$_3$.Comment: 5 pages, 6 figures. To appear in PR

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

Heat Conduction Process on Community Networks as a Recommendation Model

Using heat conduction mechanism on a social network we develop a systematic method to predict missing values as recommendations. This method can treat very large matrices that are typical of internet communities. In particular, with an innovative, exact formulation that accommodates arbitrary boundary condition, our method is easy to use in real applications. The performance is assessed by comparing with traditional recommendation methods using real data.Comment: 4 pages, 2 figure

On Birch and Swinnerton-Dyer's cubic surfaces

In a 1975 paper of Birch and Swinnerton-Dyer, a number of explicit norm form cubic surfaces are shown to fail the Hasse Principle. They make a correspondence between this failure and the Brauer--Manin obstruction, recently discovered by Manin. We generalize their work, making use of modern computer algebra software to show that a larger set of cubic surfaces have a Brauer--Manin obstruction to the Hasse principle, thus verifying the Colliot-Th\'el\`ene--Sansuc conjecture for infinitely many cubic surfaces