Quantum corrections to the thermodynamic potential of interacting Bosons in a trap

We calculate the quantum corrections of the thermodynamic quantities of a system of confined Bosons at finite temperature. Systematically quantum corrections are written in a series of $\hbar$, which is convergent when $kT$ is much larger than the spacing between energy levels of the system. We apply this method to calculate analytically the thermodynamic potential of a weakly interacting Bose-gas confined in 3-d harmonic oscillator potential. For large number of particles, quantum corrections become small, and contribute to the finite size corrections to scaling.Comment: RevTEX file (4 pages), 2 .eps figures include

Splitting between quadrupole modes of dilute quantum gas in a two dimensional anisotropic trap

We consider quadrupole excitations of quasi-two dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For two dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach.Comment: 8 pages, 3 ps figs, to appear in The European Physical Journal

Trapped two-dimensional condensates with synthetic spin-orbit coupling

We study trapped 2D atomic Bose-Einstein condensates with spin-independent interactions in the presence of an isotropic spin-orbit coupling, showing that a rich physics results from the non-trivial interplay between spin-orbit coupling, confinement and inter-atomic interactions. For low interactions two types of half-vortex solutions with different winding occur, whereas strong-enough repulsive interactions result in a stripe-phase similar to that predicted for homogeneous condensates. Intermediate interaction regimes are characterized for large enough spin-orbit coupling by an hexagonally-symmetric phase with a triangular lattice of density minima similar to that observed in rapidly rotating condensates.Comment: 4 pages, 3 figures,reduced the resolution of figure 1 from previous submissio

A new non-perturbative approach to Quantum Brownian Motion

Starting from the Caldeira-Leggett (CL) model, we derive the equation describing the Quantum Brownian motion, which has been originally proposed by Dekker purely from phenomenological basis containing extra anomalous diffusion terms. Explicit analytical expressions for the temperature dependence of the diffusion constants are derived. At high temperatures, additional momentum diffusion terms are suppressed and classical Langivin equation can be recovered and at the same time positivity of the density matrix(DM) is satisfied. At low temperatures, the diffusion constants have a finite positive value, however, below a certain critical temperature, the Master Equation(ME) does not satisfy the positivity condition as proposed by Dekker.Comment: 5 page

Rotating fermions in two dimensions: Thomas Fermi approach

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas-Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactly solved. We derive analytical expressions for the density, the critical size as well as the ground state energy of such systems in a given angular momentum sector.Comment: Latex 15 pages, 3 ps. figures. Poster in SCES-Y2K, held at SAHA Institute of Nuclear Physics,Calcutta,October (2000

Structural Transitions in A Crystalline Bilayer : The Case of Lennard Jones and Gaussian Core Models

We study structural transitions in a system of interacting particles arranged as a crystalline bilayer, as a function of the density $\rho$ and the distance $d$ between the layers. As $d$ is decreased a sequence of transitions involving triangular, rhombic, square and centered rectangular lattices is observed. The sequence of phases and the order of transitions depends on the nature of interactions.Comment: 11 pages,6 figure

Dynamic instability of a rotating Bose-Einstein condensate

We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.Comment: 4 pages, 3 figures, last version including comparison with experiment

Large Mass Diphotons From Relativistic Heavy Ion Collisions

We evaluate the production of large mass diphotons from quark annihilation at BNL RHIC and CERN LHC energies from central collisions of gold nuclei. The collision is assumed to lead to either a thermally and chemically equilibrated quark gluon plasma, or a free-streaming quark gluon gas having an identical initial entropy, or a chemically equilibrating quark gluon system, with the same entropy at $T=T_c$. We also obtain an estimate of hard photon pairs from initial state quark annihilation and find that the thermal production dominates the yield up to $M \approx$ 4 GeV at RHIC, and up to 6 GeV at LHC. A simulation study of decay versus thermal diphotons is presented.Comment: Latex file; to appear in Physics Letters