Critical behaviours of contact near phase transitions

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviors, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviors in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.Comment: Final version published in Nat. Commun. 5:5140 doi: 10.1038/ncomms6140 (2014

Transport properties and anisotropy in rare earth doped CaFe2As2 single crystals with Tc above 40 K

In this paper we report the superconductivity above 40 K in the electron doping single crystal Ca1-xRexFe2As2 (Re = La, Ce, Pr). The x-ray diffraction patterns indicate high crystalline quality and c-axis orientation. the resistivity anomaly in the parent compound CaFe2As2 is completely suppressed by partial replacement of Ca by rare earth and a superconducting transition reaches as high as 43 K, which is higher than the value in electron doping FeAs-122 compounds by substituting Fe ions with transition metal, even surpasses the highest values observed in hole doping systems with a transition temperature up to 38 K. The upper critical field has been determined with the magnetic field along ab-plane and c-axis, yielding the anisotropy of 2~3. Hall-effect measurements indicate that the conduction in this material is dominated by electron like charge carriers. Our results explicitly demonstrate the feasibility of inducing superconductivity in Ca122 compounds via electron doping using aliovalent rare earth substitution into the alkaline earth site, which should add more ingredients to the underlying physics of the iron-based superconductors.Comment: 21 pages, 7 figure

Topological aspect of graphene physics

Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is described by the Berry connection of a manybody state by the filled Landau levels which naturally possesses non-Abelian gauge structures. A generic principle of the topologically non trivial states as the bulk-edge correspondence is applied for graphene with/without magnetic field and explain some of the characteristic boundary phenomena of graphene.Comment: 12 pages, 8 figures. Proceedings for HMF-1

Microscopic origin of local moments in a zinc-doped high-TcT_{c} superconductor

The formation of a local moment around a zinc impurity in the high-$T_{c}$ cuprate superconductors is studied within the framework of the bosonic resonating-valence-bond (RVB) description of the $t-J$ model. A topological origin of the local moment has been shown based on the phase string effect in the bosonic RVB theory. It is found that such an $S=1/2$ moment distributes near the zinc in a form of staggered magnetic moments at the copper sites. The corresponding magnetic properties, including NMR spin relaxation rate, uniform spin susceptibility, and dynamic spin susceptibility, etc., calculated based on the theory, are consistent with the experimental measurements. Our work suggests that the zinc substitution in the cuprates provide an important experimental evidence for the RVB nature of local physics in the original (zinc free) state.Comment: The topological reason of local moment formation is given. One figure is adde

Some integral inequalities on time scales

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.Comment: 8 page

Summer Upwelling in the Northern Continental Shelf of the South China Sea

Summer upwelling system in the northern continental shelf of the South China Sea (NCSCS) is investigated with the Pathfinder, Advanced Very High Resolution Radiometer (AVHRR) Sea Surface Temperature (SST), and a three-dimensional, baroclinic, non-linear, numerical model forced by QuikSCAT winds. The AVHRR observation and modelling results have shown the upwelling is a regular phenomenon during summer in the NCSCS. Continental shelf upwelling characteristics are clearly found in the surface and subsurface water, such as low temperature, high salinity and high potential density. They respectively locate in the east of the Hainan Island, the east of the Leizhou Peninsula and the southeast of the Zhanjiang Bay (Qiongdong Upwelling), and the inshore areas from the Shantou Coast to the Nanri Islands of Fujian Coast (Yuedong Upwelling). The centra of the upwelling are mostly located in 111°10′E、19°45′N between the Qinglan Bay and the Qizhou Archipelagoes of eastern Hainan Island, 110°15′E、18°25′N near the Lingshui Bay, 116°45′E、22°50′N of the Shantou Coast and 118°E、23°40′N near the Taiwan Shoal. It is also found that the upwelling areas and centra from modelling results are in agreement with the AVHRR SST

Strong subconvexity for self-dual GL(3)\mathrm{GL} (3) LL-functions

In this paper, we prove strong subconvexity bounds for self-dual $\mathrm{GL}(3)$ $L$-functions in the $t$-aspect and for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ $L$-functions in the $\mathrm{GL}(2)$-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pioneered by Xiaoqing Li, modulo current knowledge on estimate for the second moment of $\rm GL(3)$ $L$-functions on the critical line