A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions

In this paper, the fractional order of rational Bessel functions collocation method (FRBC) to solve Thomas-Fermi equation which is defined in the semi-infinite domain and has singularity at $x = 0$ and its boundary condition occurs at infinity, have been introduced. We solve the problem on semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration solves it by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results in other to show that the new method is accurate, efficient and applicable

Scattering of short laser pulses from trapped fermions

We investigate the scattering of intense short laser pulses off trapped cold fermionic atoms. We discuss the sensitivity of the scattered light to the quantum statistics of the atoms. The temperature dependence of the scattered light spectrum is calculated. Comparisons are made with a system of classical atoms who obey Maxwell-Boltzmann statistics. We find the total scattering increases as the fermions become cooler but eventually tails off at very low temperatures (far below the Fermi temperature). At these low temperatures the fermionic degeneracy plays an important role in the scattering as it inhibits spontaneous emission into occupied energy levels below the Fermi surface. We demonstrate temperature dependent qualitative changes in the differential and total spectrum can be utilized to probe quantum degeneracy of trapped Fermi gas when the total number of atoms are sufficiently large $(\geq 10^6)$. At smaller number of atoms, incoherent scattering dominates and it displays weak temperature dependence.Comment: updated figures and revised content, submitted to Phys.Rev.

Nonparametric Identification and Estimation of Multi-Unit, Sequential, Oral, Ascending-Price Auctions With Asymmetric Bidders

Within the independent private-values paradigm, we derive the data-generating process of the winning bid for the last unit sold at multi-unit sequential English auctions when bidder valuations are draws from different distributions; i.e., in the presence of asymmetries. When the identity of the winner as well as the number of units won by each bidder in previous stages of the auction are observed, we demonstrate nonparametric identification and then propose two estimation strategies, one based on the empirical distribution function of winning bids for the last unit sold and the other based on approximation methods using orthogonal polynomials. We apply our methods to daily data from fish auctions held in Grenå, Denmark. For single-unit supply, we use our estimates to compare the revenues a seller could expect to earn were a Dutch auction employed instead.Asymmetric, Multi-unit, Sequential, Oral, Ascending-price fish auctions, Dutch auctions, Nonparametric identification and estimation