The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behavior, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behavior of the isochore heat capacity for a trapped unitary Fermi gas is also analyzed.Comment: 6 pages, 6 figure

Fast orthogonal least squares algorithm for efficient subset model selection

Abstract-An efficient implementation of the orthogonal least squares algorithm for subset model selection is derived in this correspondence. Computational complexity of the algorithm is examined and the result shows that this new fast orthogonal least squares algorithm significantly reduces computational requirements. This error reduction ratio provides a criterion for forward subset selection. At the beginning of the 11th stage of the selection procedure, X has been transformed into X”’- ” = [WI... wI,- I xj,’-’)... x::;-’)] and y into y(/’-’), The 11th stage consists of i) For p 5 j 5.If, compute ii) 1

Mapping class group and U(1) Chern-Simons theory on closed orientable surfaces

U(1) Chern-Simons theory is quantized canonically on manifolds of the form $M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In particular, we investigate the role of mapping class group of $\Sigma$ in the process of quantization. We show that, by requiring the quantum states to form representation of the holonomy group and the large gauge transformation group, both of which are deformed by quantum effect, the mapping class group can be consistently represented, provided the Chern-Simons parameter $k$ satisfies an interesting quantization condition. The representations of all the discrete groups are unique, up to an arbitrary sub-representation of the mapping class group. Also, we find a $k\leftrightarrow1/k$ duality of the representations.Comment: 17 pages, 3 figure

Ground state energy of unitary fermion gas with the Thomson Problem approach

The dimensionless universal coefficient $\xi$ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson Problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be $\xi={4/9}$. The energy gap is \Delta=\frac{{5}{18}{k_f^2}/(2m).Comment: Identical to published version with revisions according to comment

Forced sloshing of inviscid fluids

Forced sloshing motion of inviscid fluids in rigid cylinder

Online Matrix Completion Through Nuclear Norm Regularisation

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the Soft Impute approach introduced in Mazumder et al. (2010). The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.Comment: Corrected a typo in the affiliatio

Searching for radiative pumping lines of OH masers: II. The 53.3um absorption line towards 1612MHz OH maser sources

This paper analyzes the 53.3um line in the ISO LWS spectra towards a similar sample of OH/IR sources. We find 137 LWS spectra covering 53.3um and associated with 47 galactic OH/IR sources. Ten of these galactic OH/IR sources are found to show and another 5 ones tentatively show the 53.3um absorption while another 7 sources highly probably do not show this line. The source class is found to be correlated with the type of spectral profile: red supergiants (RSGs) and AGB stars tend to show strong blue-shifted filling emission in their 53.3um absorption line profiles while HII regions tend to show a weak red-shifted filling emission in the line profile. GC sources and megamasers do not show filling emission feature. It is argued that the filling emission might be the manifestation of an unresolved half emission half absorption profile of the 53.3um doublet. The 53.3 to 34.6um equivalent width (EW) ratio is close to unity for RSGs but much larger than unity for GC sources and megamasers while H II regions only show the 53.3um line. The pump rate defined as maser to IR photon flux ratio is approximately 5% for RSGs. The pump rates of GC sources are three order of magnitude smaller. Both the large 53.3 to 34.6um EW ratio and the small pump rate of the GC OH masers reflect that the two detected `pumping lines' in these sources are actually of interstellar origin. The pump rate of Arp 220 is 32%--much larger than that of RSGs, which indicates that the contribution of other pumping mechanisms to this megamaser is important.Comment: 34 pages, 12 figures, 4 table