Are there compact heavy four-quark bound states?

We present an exact method to study four-quark systems based on the hyperspherical harmonics formalism. We apply it to several physical systems of interest containing two heavy and two light quarks using different quark-quark potentials. Our conclusions mark the boundaries for the possible existence of compact, non-molecular, four-quark bound states. While $QQ\bar n \bar n$ states may be stable in nature, the stability of $Q\bar Qn \bar n$ states would imply the existence of quark correlations not taken into account by simple quark dynamical modelsComment: 10 pages, 1 figure. Accepted for publication in Phys. Rev.

The two-atom energy spectrum in a harmonic trap near a Feshbach resonance at higher partial waves

Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal $l=2$ energy spectrum for such a system, with a caveat, is presented in this paper, and checked with the spectrum obtained by direct numerical integration of the Schr\"odinger equation. The results reported here extend those of Yip for p-wave resonance (Phys. Rev. A {\bf 78}, 013612 (2008)), while exploring the limitations of a universal expression for the spectrum for the higher partial waves.Comment: To be published in Physical Review

Production and detection of doubly charmed tetraquarks

The feasibility of tetraquark detection is studied. For the cc\bar{u}\bar{d} tetraquark we show that in present (SELEX, Tevatron, RHIC) and future facilities (LHCb, ALICE) the production rate is promising and we propose some detectable decay channels.Comment: 6 pages, 5 figure

Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis

Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic collocation method with adaptive mesh refinement (SCAMR) to deal with high dimensional stochastic systems with discontinuities. Specifically, the proposed approach uses generalized polynomial chaos (gPC) expansion with Legendre polynomial basis and solves for the gPC coefficients using the least squares method. It also implements an adaptive mesh (element) refinement strategy which checks for abrupt variations in the output based on the second order gPC approximation error to track discontinuities or non-smoothness. In addition, the proposed method involves a criterion for checking possible dimensionality reduction and consequently, the decomposition of the full-dimensional problem to a number of lower-dimensional subproblems. Specifically, this criterion checks all the existing interactions between input dimensions of a specific problem based on the high-dimensional model representation (HDMR) method, and therefore automatically provides the subproblems which only involve interacting dimensions. The efficiency of the approach is demonstrated using both smooth and non-smooth function examples with input dimensions up to 300, and the approach is compared against other existing algorithms

An ansatz for the exclusion statistics parameters in macroscopic physical systems described by fractional exclusion statistics

I introduce an ansatz for the exclusion statistics parameters of fractional exclusion statistics (FES) systems and I apply it to calculate the statistical distribution of particles from both, bosonic and fermionic perspectives. Then, to check the applicability of the ansatz, I calculate the FES parameters in three well-known models: in a Fermi liquid type of system, a one-dimensional quantum systems described in the thermodynamic Bethe ansatz and quasiparticle excitations in the fractional quantum Hall (FQH) systems. The FES parameters of the first two models satisfy the ansatz, whereas those of the third model, although close to the form given by the ansatz, represent an exception. With this ocasion I also show that the general properties of the FES parameters, deduced elsewhere (EPL 87, 60009, 2009), are satisfied also by the parameters of the FQH liquid.Comment: 6 pages, EPL styl

Zeta Function Zeros, Powers of Primes, and Quantum Chaos

We present a numerical study of Riemann's formula for the oscillating part of the density of the primes and their powers. The formula is comprised of an infinite series of oscillatory terms, one for each zero of the zeta function on the critical line and was derived by Riemann in his paper on primes assuming the Riemann hypothesis. We show that high resolution spectral lines can be generated by the truncated series at all powers of primes and demonstrate explicitly that the relative line intensities are correct. We then derive a Gaussian sum rule for Riemann's formula. This is used to analyze the numerical convergence of the truncated series. The connections to quantum chaos and semiclassical physics are discussed