High temperature expansion applied to fermions near Feshbach resonance

We show that, apart from a difference in scale, all of the surprising recently observed properties of a degenerate Fermi gas near a Feshbach resonance persist in the high temperature Boltzmann regime. In this regime, the Feshbach resonance is unshifted. By sweeping across the resonance, a thermal distribution of bound states (molecules) can be reversibly generated. Throughout this process, the interaction energy is negative and continuous. We also show that this behavior must persist at lower temperatures unless there is a phase transition as the temperature is lowered. We rigorously demonstrate universal behavior near the resonance.Comment: 4 pages, 4 figures (3 color, 1 BW), RevTeX4; ver4 -- updated references, changed title -- version accepted for publication in Physical Review Letter

Theory and application of Fermi pseudo-potential in one dimension

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer.Comment: RevTeX4, 32 pages, no figure

Studies on electrostatic interactions of colloidal particles under two-dimensional confinement

We study the effective electrostatic interactions between a pair of charged colloidal particles without salt ions while the system is confined in two dimensions. In particular we use a simplified model to elucidate the effects of rotational fluctuations in counterion distribution. The results exhibit effective colloidal attractions under appropriate conditions. Meanwhile, long-range repulsions persist over most of our studied cases. The repulsive forces arise from the fact that in two dimensions the charged colloids cannot be perfectly screened by counterions, as the residual quadrupole moments contribute to the repulsions at longer range. And by applying multiple expansions we find that the attractive forces observed at short range are mainly contributed from electrostatic interactions among higher-order electric moments. We argue that the scenario for attractive interactions discussed in this work is applicable to systems of charged nanoparticles or colloidal solutions with macroions.Comment: 23 pages, 11 figures, 1 tabl

1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations

Infrastructure for genomic interactions: Bioconductor classes for Hi-C, ChIA-PET and related experiments [version 1; referees: 2 approved]

The study of genomic interactions has been greatly facilitated by techniques such as chromatin conformation capture with high-throughput sequencing (Hi-C). These genome-wide experiments generate large amounts of data that require careful analysis to obtain useful biological conclusions. However, development of the appropriate software tools is hindered by the lack of basic infrastructure to represent and manipulate genomic interaction data. Here, we present the InteractionSet package that provides classes to represent genomic interactions and store their associated experimental data, along with the methods required for low-level manipulation and processing of those classes. The InteractionSet package exploits existing infrastructure in the open-source Bioconductor project, while in turn being used by Bioconductor packages designed for higher-level analyses. For new packages, use of the functionality in InteractionSet will simplify development, allow access to more features and improve interoperability between packages.Cancer Research UK (Grant ID: A17197)This is the final version of the article. It first appeared from F1000 Research via http://dx.doi.org/10.12688/f1000research.8759.

Phase Separation in Mixtures of Repulsive Fermi Gases Driven by Mass Difference

We show that phase separation must occur in a mixture of fermions with repulsive interaction if their mass difference is sufficiently large. This phenomenon is highly dimension-dependent. Consequently, the density profiles of phase separated 3d mixtures are very different from those in 1d. Noting that the ferromagnetic transition of a spin-1/2 repulsive Fermi gas is the equal mass limit of the phase separation in mixtures, we show from the Bethe Ansatz solution that a ferromagnetic transition will take place in the scattering states when the repulsive interaction passes through resonance and becomes attractive.Comment: 4.5 pages, 2 figures, version accepted by Phys. Rev. Let

Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy

We study the exchange of kinetic energy between translational and rotational degrees of freedom for inelastic collisions of rough spheres. Even if equipartition holds in the initial state it is immediately destroyed by collisions. The simplest generalisation of the homogeneous cooling state allows for two temperatures, characterizing translational and rotational degrees of freedom separately. For times larger than a crossover frequency, which is determined by the Enskog frequency and the initial temperature, both energies decay algebraically like $t^{-2}$ with a fixed ratio of amplitudes, different from one.Comment: 5 pages, RevTeX, 2 eps figures, slightly expanded discussion, new figures with dimensionless units, added references, accepted for publication in PRE as a Rapid Com

Boro/carbothermal Reduction Co-Synthesis of Dual-Phase High-Entropy Boride-Carbide Ceramics

Dense, dual-phase (Cr,Hf,Nb,Ta,Ti,Zr)B2-(Cr,Hf,Nb,Ta,Ti,Zr)C ceramics were synthesized by boro/carbothermal reduction of oxides and densified by spark plasma sintering. The high-entropy carbide content was about 14.5 wt%. Grain growth was suppressed by the pinning effect of the two-phase ceramic, which resulted in average grain sizes of 2.7 ± 1.3 µm for the high-entropy boride phase and 1.6 ± 0.7 µm for the high-entropy carbide phase. Vickers hardness values increased from 25.2 ± 1.1 GPa for an indentation load of 9.81 N to 38.9 ± 2.5 GPa for an indentation load of 0.49 N due to the indentation size effect. Boro/carbothermal reduction is a facile process for the synthesis and densification of dual-phase high entropy boride-carbide ceramics with both different combinations of transition metals and different proportions of boride and carbide phases