Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunneling between two trapped Bose-Einstein condensates is shown to admit an exact solution. The spectrum is obtained by the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and first excited states in the limit of {\it weak} tunneling and all energies for {\it strong} tunneling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.Comment: 5 pages, RevTex, No figure

Hole Doping Dependence of the Coherence Length in La2−xSrxCuO4La_{2-x}Sr_xCuO_4 Thin Films

By measuring the field and temperature dependence of magnetization on systematically doped $La_{2-x}Sr_xCuO_4$ thin films, the critical current density $j_c(0)$ and the collective pinning energy $U_p(0)$ are determined in single vortex creep regime. Together with the published data of superfluid density, condensation energy and anisotropy, for the first time we derive the doping dependence of the coherence length or vortex core size in wide doping regime directly from the low temperature data. It is found that the coherence length drops in the underdoped region and increases in the overdoped side with the increase of hole concentration. The result in underdoped region clearly deviates from what expected by the pre-formed pairing model if one simply associates the pseudogap with the upper-critical field.Comment: 4 pages, 4 figure

Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection

Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with $m$ arms in Rayleigh-Benard convection are obtained. Global spirals and parallel rolls share exactly the same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals seem not to have a characteristic frequency $\omega_m$ or a typical size $R_m$, but their product $\omega_m R_m$ is a constant under given experimental conditions. The ratio $R_i/R_j$ of the radii of any two dislocations ($R_i$, $R_j$) inside a multi-armed spiral is also predicted to be constant. Some of these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication

Quantum Criticality of 1D Attractive Fermi Gas

We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gas for all parameter regime in current experiments. From the equation of state we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate physical origin of quantum criticality. It turns out that the critical properties of the system are described by these of free fermions and those of mixtures of fermions with mass $m$ and $2m$. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gas at finite temperatures and can be used to determine the T=0 phase boundaries without any arbitrariness.Comment: extended version, 9 pages, 7 eps figures, corrections of few typo

Wilson Ratio of Fermi gases in One Dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-compone

Enhanced Orbital Degeneracy in Momentum Space for LaOFeAs

The Fermi surfaces (FS) of LaOFeAs (in $k_z$=0 plane) consist of two hole-type circles around $\Gamma$ point, which do not touch each other, and two electron-type co-centered ellipses around M point, which are degenerate along the M-X line. By first-principles calculations, here we show that additional degeneracy exists for the two electron-type FS, and the crucial role of F-doping and pressure is to enhance this orbital degeneracy. It is suggested that the inter-orbital fluctuation is the key point to understand the unconventional superconductivity in these materials.Comment: 4 pages, 5 figure

Single chargino production via gluon-gluon fusion in a supersymmetric theory with an explicit R-parity violation

We studied the production of single chargino$\tilde{\chi}_1^{\pm}$ accompanied by $\mu^{\mp}$ lepton via gluon-gluon fusion at the LHC. The numerical analysis of their production rates is carried out in the mSUGRA scenario with some typical parameter sets. The results show that the cross sections of the $\tilde{\chi}_1^{\pm}\mu^{\mp}$ productions via gluon-gluon collision are in the order of $1 \sim 10^{2}$ femto barn quantitatively at the CERN LHC, and can be competitive with production mechanism via quark-antiquark annihilation process.Comment: LaTex file, 18 pages, 4 EPS file

Lipschitz equivalence of subsets of self-conformal sets

We give sufficient conditions to guarantee that if two self-conformal sets E and F have Lipschitz equivalent subsets of positive measure, then there is a bilipschitz map of E into, or onto, F

One-dimensional multicomponent fermions with delta function interaction in strong and weak coupling limits: Two-component Fermi gas

The Fredholm equations for one-dimensional two-component Fermions with repulsive and with attractive delta-function interactions are solved by an asymptotic expansion for A) strong repulsion, B) weak repulsion, C) weak attraction and D) strong attraction. Consequently, we obtain the first few terms of the expansion of ground state energy for the Fermi gas with polarization for these regimes. We also prove that the two sets of the Fredhom equations for weakly repulsive and attractive interactions are identical as long as the integration boundaries match each other between the two sides. Thus the asymptotic expansions of the energies of the repulsive and attractive Fermions are identical to all orders in this region. The identity of the asymptotic expansions may not mean that the energy analytically connects.Comment: 2 figures, 10 page