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

Local Regularization Assisted Orthogonal Least Squares Regression

A locally regularized orthogonal least squares (LROLS) algorithm is proposed for constructing parsimonious or sparse regression models that generalize well. By associating each orthogonal weight in the regression model with an individual regularization parameter, the ability for the orthogonal least squares (OLS) model selection to produce a very sparse model with good generalization performance is greatly enhanced. Furthermore, with the assistance of local regularization, when to terminate the model selection procedure becomes much clearer. This LROLS algorithm has computational advantages over the recently introduced relevance vector machine (RVM) method

Gibbsian Hypothesis in Turbulence

We show that Kolmogorov multipliers in turbulence cannot be statistically independent of others at adjacent scales (or even a finite range apart) by numerical simulation of a shell model and by theory. As the simplest generalization of independent distributions, we suppose that the steady-state statistics of multipliers in the shell model are given by a translation-invariant Gibbs measure with a short-range potential, when expressed in terms of suitable ``spin'' variables: real-valued spins that are logarithms of multipliers and XY-spins defined by local dynamical phases. Numerical evidence is presented in favor of the hypothesis for the shell model, in particular novel scaling laws and derivative relations predicted by the existence of a thermodynamic limit. The Gibbs measure appears to be in a high-temperature, unique-phase regime with ``paramagnetic'' spin order.Comment: 19 pages, 9 figures, greatly expanded content, accepted to appear in J. Stat. Phy

Strongly Coupled Inflaton

We continue to investigate properties of the strongly coupled inflaton in a setup introduced in arXiv:0807.3191 through the AdS/CFT correspondence. These properties are qualitatively different from those in conventional inflationary models. For example, in slow-roll inflation, the inflaton velocity is not determined by the shape of potential; the fine-tuning problem concerns the dual infrared geometry instead of the potential; the non-Gaussianities such as the local form can naturally become large.Comment: 12 pages; v3, minor revision, comments and reference added, JCAP versio

Stability Of contact discontinuity for steady Euler System in infinite duct

In this paper, we prove structural stability of contact discontinuities for full Euler system

Driving Operators Relevant: A Feature of Chern-Simons Interaction

By computing anomalous dimensions of gauge invariant composite operators $(\bar\psi\psi)^n$ and $(\phi^*\phi)^n$ in Chern-Simons fermion and boson models, we address that Chern-Simons interactions make these operators more relevant or less irrelevant in the low energy region. We obtain a critical Chern-Simons fermion coupling, ${1\over \kappa_c^2} = {6\over 19}$, for a phase transition at which the leading irrelevant four-fermion operator $(\bar\psi\psi)^2$ becomes marginal, and a critical Chern-Simons boson coupling, ${1\over \kappa_c^2} = {6\over 34}$, for a similar phase transition for the leading irrelevant operator $(\phi^*\phi)^4$. We see this phenomenon also in the $1/N$ expansion.Comment: (ten pages, latex, figures included