Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Let $\mathcal{L}_\epsilon$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1,p}$ estimate in a Lipschitz domain for solutions to the Dirichlet problem, where $(2n/(n+1)) -\delta<p<(2n/(n-1))+\delta$. The ranges of $p$'s are sharp for $n=2$ or 3

Hyperfine Spin-Two (F=2) Atoms in Three-Dimensional Optical Lattices: Phase Diagrams and Phase Transitions

We consider ultracold matter of spin-2 atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian in an on-site Hilbert space taking into account spin-dependent interactions and exchange between different sites. We obtain phase diagrams and quantum phase transitions between various magnetic phases.Comment: 10 pages, 10 figures, published versio

Quark charge balance function and hadronization effects in relativistic heavy ion collisions

We calculate the charge balance function of the bulk quark system before hadronization and those for the directly produced and the final hadron system in high energy heavy ion collisions. We use the covariance coefficient to describe the strength of the correlation between the momentum of the quark and that of the anti-quark if they are produced in a pair and fix the parameter by comparing the results for hadrons with the available data. We study the hadronization effects and decay contributions by comparing the results for hadrons with those for the bulk quark system. Our results show that while hadronization via quark combination mechanism slightly increases the width of the charge balance functions, it preserves the main features of these functions such as the longitudinal boost invariance and scaling properties in rapidity space. The influence from resonance decays on the width of the balance function is more significant but it does not destroy its boost invariance and scaling properties in rapidity space either. The balance functions in azimuthal direction are also presented.Comment: 9 figure

Tunable Quantum Fluctuation-Controlled Coherent Spin Dynamics

Temporal evolution of a macroscopic condensate of ultra cold atoms is usually driven by mean field potentials, either due to scattering between atoms or due to coupling to external fields; and coherent quantum dynamics have been observed in various cold-atom experiments. In this article, we report results of studies of a class of quantum spin dynamics which are purely driven by zero point quantum fluctuations of spin collective coordinates. Unlike the usual mean-field coherent dynamics, quantum fluctuation-controlled spin dynamics or QFCSD studied here are very sensitive to variation of quantum fluctuations and can be tuned by four to five order of magnitude using optical lattices. They have unique dependence on optical lattice potential depths and quadratic Zeeman fields. QFCSD can be potentially used to calibrate quantum fluctuations and investigate correlated fluctuations and various universal scaling properties near quantum critical points.Comment: 14 pages, 12 figures included; including detailed discussions on thermal effects, trapping potentials and spin exchange losses. (To appear in PRA

Quantum fluctuation-induced uniaxial and biaxial spin nematics

It is shown that zero point quantum fluctuations (ZPQFs) completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin 2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry ${Dih}_4$. There is a novel first order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of $^{87}Rb$ atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments.Comment: 4 pages, 2 figures included; published versio

Quark number scaling of hadronic pTp_T spectra and constituent quark degree of freedom in pp-Pb collisions at sNN=5.02\sqrt{s_{NN}}=5.02 TeV

We show that the experimental data of $p_T$ spectra of identified hadrons released recently by ALICE collaboration for $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV exhibit a distinct universal behavior --- the quark number scaling. We further show that the scaling is a direct consequence of quark (re-)combination mechanism of hadronization and can be regarded as a strong indication of the existence of the underlying source with constituent quark degree of freedom for the production of hadrons in $p$-Pb collisions at such high energies. We make also predictions for production of other hadrons.Comment: 5 pages, 3 figure