Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence

Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation

Decay rate of a Wannier exciton in low dimensional systems

The superradiant decay rate of Wannier exciton in one dimensional system is studied. The crossover behavior from 1D chain to 2D film is also examined. It is found that the decay rate shows oscillatory dependence on channel width L. When the quasi 1-D channel is embeded with planar microcavities, it is shown that the dark mode exciton can be examined experimentally.Comment: 12 pages, 1 figur

Nonmonotonic External Field Dependence of the Magnetization in a Finite Ising Model: Theory and MC Simulation

Using $\phi^4$ field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization $M$ for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state $h/M^\delta = f(hL^{\beta\delta/\nu}, t/h^{1/\beta\delta})$ where $t=(T-T_c)/T_c$ is the reduced temperature, $h$ is the external field and $L$ is the size of system. Below $T_c$ and at $T_c$ the theory predicts a nonmonotonic dependence of $f(x,y)$ with respect to $x \equiv hL^{\beta\delta/\nu}$ at fixed $y \equiv t/h^{1/\beta \delta}$ and a crossover from nonmonotonic to monotonic behaviour when $y$ is further increased. These results are confirmed by MC simulation. The scaling function $f(x,y)$ obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value $f(\infty,0)$ at $T_c$.Comment: LaTex, 12 page

Formation of ultracold LiRb molecules by photoassociation near the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote

We report the production of ultracold 7Li85Rb molecules by photoassociation (PA) below the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We perform PA spectroscopy in a dual-species 7Li-85Rb magneto-optical trap (MOT) and detect the PA resonances using trap loss spectroscopy. We observe several strong PA resonances corresponding to the last few bound states, assign the lines and derive the long range C6 dispersion coefficients for the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We also report an excited-state molecule formation rate (P_LiRb) of ~10^7 s^-1 and a PA rate coefficient (K_PA) of ~4x10^-11 cm^3/s, which are both among the highest observed for heteronuclear bi-alkali molecules. These suggest that PA is a promising route for the creation of ultracold ground state LiRb molecules.Comment: 6 page

A connection between the Camassa-Holm equations and turbulent flows in channels and pipes

In this paper we discuss recent progress in using the Camassa-Holm equations to model turbulent flows. The Camassa-Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa-Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggests that the constant $\alpha$ version of the Camassa-Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order $\alpha$ distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale $\alpha$ is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant $\alpha$ region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that $\alpha$ decreases as Reynolds number increases. Away from boundaries, these scaling conditions imply $\alpha$ is independent of Reynolds number. Given the agreement with empirical and numerical data, our current work indicates that the Camassa-Holm equations provide a promising theoretical framework from which to understand some turbulent flows.Comment: tex file, 29 pages, 4 figures, Physics of Fluids (in press

Non-universal size dependence of the free energy of confined systems near criticality

The singular part of the finite-size free energy density $f_s$ of the O(n) symmetric $\phi^4$ field theory in the large-n limit is calculated at finite cutoff for confined geometries of linear size L with periodic boundary conditions in 2 < d < 4 dimensions. We find that a sharp cutoff $\Lambda$ causes a non-universal leading size dependence $f_s \sim \Lambda^{d-2} L^{-2}$ near $T_c$ which dominates the universal scaling term $\sim L^{-d}$. This implies a non-universal critical Casimir effect at $T_c$ and a leading non-scaling term $\sim L^{-2}$ of the finite-size specific heat above $T_c$.Comment: RevTex, 4 page

Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy

By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.Comment: 9 page