Transition Temperature of a Uniform Imperfect Bose Gas

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a is the S-wave scattering length, and K_0 is a constant given in the paper. This disagrees with all existing results, analytical or numerical. It agrees exactly in magnitude with a result due to Toyoda, but has the opposite sign.Comment: Email correspondence to [email protected] ; 2 pages using REVTe

Convective flow during dendritic growth

A review is presented of the major experimental findings obtained from recent ground-based research conducted under the SPAR program. Measurements of dendritic growth at small supercoolings indicate that below approximately 1.5 K a transition occurs from diffusive control to convective control in succinonitrile, a model system chosen for this study. The key theoretical ideas concerning diffusive and convective heat transport during dendritic growth are discussed, and it is shown that a transition in the transport control should occur when the characteristic length for diffusion becomes larger than the characteristic length for convection. The experimental findings and the theoretical ideas discussed suggest that the Fluid Experiment System could provide appropriate experimental diagnostics for flow field visualization and quantification of the fluid dynamical effects presented here

Localization Transition in Incommensurate non-Hermitian Systems

A class of one-dimensional lattice models with incommensurate complex potential $V(\theta)=2[\lambda_r cos(\theta)+i \lambda_i sin(\theta)]$ is found to exhibit localization transition at $|\lambda_r|+|\lambda_i|=1$. This transition from extended to localized states manifests in the behavior of the complex eigenspectum. In the extended phase, states with real eigenenergies have finite measure and this measure goes to zero in the localized phase. Furthermore, all extended states exhibit real spectrum provided $|\lambda_r| \ge |\lambda_i|$. Another novel feature of the system is the fact that the imaginary part of the spectrum is sensitive to the boundary conditions {\it only at the onset to localization}

Density of states of a graphene in the presence of strong point defects

The density of states near zero energy in a graphene due to strong point defects with random positions are computed. Instead of focusing on density of states directly, we analyze eigenfunctions of inverse T-matrix in the unitary limit. Based on numerical simulations, we find that the squared magnitudes of eigenfunctions for the inverse T-matrix show random-walk behavior on defect positions. As a result, squared magnitudes of eigenfunctions have equal {\it a priori} probabilities, which further implies that the density of states is characterized by the well-known Thomas-Porter type distribution. The numerical findings of Thomas-Porter type distribution is further derived in the saddle-point limit of the corresponding replica field theory of inverse T-matrix. Furthermore, the influences of the Thomas-Porter distribution on magnetic and transport properties of a graphene, due to its divergence near zero energy, are also examined.Comment: 6 figure

S-wave quantum entanglement in a harmonic trap

We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultra-cold temperature, ground state entanglement is generated by the dominated s-wave interaction. Based on a regularized pseudo-potential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified s-wave scattering length inside the trap.Comment: 10 pages, 5 figures, to be apear in PR