A Hybrid Model for QCD Deconfining Phase Boundary

Intensive search for a proper and realistic equations of state (EOS) is still continued for studying the phase diagram existing between quark gluon plasma (QGP) and hadron gas (HG) phases. Lattice calculations provide such EOS for the strongly interacting matter at finite temperature ($T$) and vanishing baryon chemical potential ($\mu_{B}$). These calculations are of limited use at finite $\mu_{B}$ due to the appearance of notorious sign problem. In the recent past, we had constructed a hybrid model description for the QGP as well as HG phases where we make use of a new excluded-volume model for HG and a thermodynamically-consistent quasiparticle model for the QGP phase and used them further to get QCD phase boundary and a critical point. Since then many lattice calculations have appeared showing various thermal and transport properties of QCD matter at finite $T$ and $\mu_{B}=0$. We test our hybrid model by reproducing the entire data for strongly interacting matter and predict our results at finite $\mu_{B}$ so that they can be tested in future. Finally we demonstrate the utility of the model in fixing the precise location, the order of the phase transition and the nature of CP existing on the QCD phase diagram. We thus emphasize the suitability of the hybrid model as formulated here in providing a realistic EOS for the strongly interacting matter.Comment: 22 pages, 10 figures. corrected version published in Physical Review D. arXiv admin note: substantial text overlap with arXiv:1201.044

Bose-Einstein Condensates in Optical Quasicrystal Lattices

We analyze the physics of Bose-Einstein condensates confined in 2D quasi-periodic optical lattices, which offer an intermediate situation between ordered and disordered systems. First, we analyze the time-of-flight interference pattern that reveals quasi-periodic long-range order. Second, we demonstrate localization effects associated with quasi-disorder as well as quasiperiodic Bloch oscillations associated with the extended nature of the wavefunction of a Bose-Einstein condensate in an optical quasicrystal. In addition, we discuss in detail the crossover between diffusive and localized regimes when the quasi-periodic potential is switched on, as well as the effects of interactions

A systematic correlation between two-dimensional flow topology and the abstract statistics of turbulence

Velocity differences in the direct enstrophy cascade of two-dimensional turbulence are correlated with the underlying flow topology. The statistics of the transverse and longitudinal velocity differences are found to be governed by different structures. The wings of the transverse distribution are dominated by strong vortex centers, whereas, the tails of the longitudinal differences are dominated by saddles. Viewed in the framework of earlier theoretical work this result suggests that the transfer of enstrophy to smaller scales is accomplished in regions of the flow dominated by saddles.Comment: 4 pages, 4 figure

A comparison of spectral element and finite difference methods using statically refined nonconforming grids for the MHD island coalescence instability problem

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (MICI) in two dimensions. MICI is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.Comment: 19 pages, 17 figures, submitted to Astrophys. J. Supp

Constraints on the Universal Varying Yukawa Couplings: from SM-like to Fermiophobic

Varying the Standard Model (SM) fermion Yukawa couplings universally by a generic positive scale factor ($F_{Yu}$), we study the phenomenological fit to the current available experimental results for the Higgs boson search at hadron colliders. We point out that the Higgs production cross section and its decay branching ratio to $\gamma\gamma$ can be varied oppositely by $F_{Yu}$ to make their product almost invariant. Thus, our scenario and the SM Higgs are indistinguishable in the inclusive $H\to \gamma\gamma$ channel. The current measurements on direct Yukawa coupling strength in the $H\to b\bar{b}/\tau\tau$ channel are not precise enough to fix the scale factor $F_{Yu}$. The most promising is the vector-boson-fusion channel in which the CMS has already observed possible suppression effect on the Yukawa couplings. Further more, the global $\chi^2$ fit of the experimental data can get the optimal value by introducing a suppression factor $F_{Yu}\sim1/2$ on the SM Yukawa couplings.Comment: 16 pages, 12 figures, 5 tables, update analysis is supplemente

Exploring \pp scattering in the \1N picture

In the large $N_c$ approximation to $QCD$, the leading \pp scattering amplitude is expressed as the sum of an infinite number of tree diagrams. We investigate the possibility that an adequate approximation at energies up to somewhat more than one $GeV$ can be made by keeping diagrams which involve the exchange of resonances in this energy range in addition to the simplest chiral contact terms. In this approach crossing symmetry is automatic but individual terms tend to drastically violate partial wave unitarity. We first note that the introduction of the $\rho$ meson in a chirally invariant manner substantially delays the onset of drastic unitarity violation which would be present for the {\it current algebra} term alone. This suggests a possibility of local (in energy) cancellation which we then explore in a phenomenological way. We include exchanges of leading resonances up to the $1.3 GeV$ region. However, unitarity requires more structure which we model by a four derivative contact term or by a low lying scalar resonance which is presumably subleading in the \1N expansion, but may nevertheless be important. The latter two flavor model gives a reasonable description of the phase shift $\delta^0_0$ up until around $860 MeV$, before the effects associated which the $K\bar{K}$ threshold come into play.Comment: 27 LaTex pages + 13 figures (also available in hard-copy

Dynamical Evolution of the Scalar Condensate in Heavy Ion Collisions

We derive the effective coarse-grained field equation for the scalar condensate of the linear sigma model in a simple and straightforward manner using linear response theory. The dissipative coefficient is calculated at tree level on the basis of the physical processes of sigma-meson decay and of thermal sigma-mesons and pions knocking sigma-mesons out of the condensate. The field equation is solved for hot matter undergoing either one or three dimensional expansion and cooling in the aftermath of a high energy nuclear collision. The results show that the time constant for returning the scalar condensate to thermal equilibrium is of order 2 fm/c.Comment: 19 pages, 3 figures are embedded at the end. The effect of the time dependence of the condensate v is included in this revised version. Numerical work is redone accordingl

Graduate Quantum Mechanics Reform

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.Comment: accepted to American Journal of Physic

On the dual cascade in two-dimensional turbulence

We study the dual cascade scenario for two-dimensional turbulence driven by a spectrally localized forcing applied over a finite wavenumber range [k_\min,k_\max] (with k_\min > 0) such that the respective energy and enstrophy injection rates $\epsilon$ and $\eta$ satisfy k_\min^2\epsilon\le\eta\le k_\max^2\epsilon. The classical Kraichnan--Leith--Batchelor paradigm, based on the simultaneous conservation of energy and enstrophy and the scale-selectivity of the molecular viscosity, requires that the domain be unbounded in both directions. For two-dimensional turbulence either in a doubly periodic domain or in an unbounded channel with a periodic boundary condition in the across-channel direction, a direct enstrophy cascade is not possible. In the usual case where the forcing wavenumber is no greater than the geometric mean of the integral and dissipation wavenumbers, constant spectral slopes must satisfy $\beta>5$ and $\alpha+\beta\ge8$, where $-\alpha$ ($-\beta$) is the asymptotic slope of the range of wavenumbers lower (higher) than the forcing wavenumber. The influence of a large-scale dissipation on the realizability of a dual cascade is analyzed. We discuss the consequences for numerical simulations attempting to mimic the classical unbounded picture in a bounded domain.Comment: 22 pages, to appear in Physica

Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya