Excited states of a static dilute spherical Bose condensate in a trap

The Bogoliubov approximation is used to study the excited states of a dilute gas of $N$ atomic bosons trapped in an isotropic harmonic potential characterized by a frequency $\omega_0$ and an oscillator length $d_0 = \sqrt{\hbar/m\omega_0}$. The self-consistent static Bose condensate has macroscopic occupation number $N_0 \gg 1$, with nonuniform spherical condensate density $n_0(r)$; by assumption, the depletion of the condensate is small ($N' \equiv N - N_0\ll N_0$). The linearized density fluctuation operator $\hat \rho'$ and velocity potential operator $\hat\Phi'$ satisfy coupled equations that embody particle conservation and Bernoulli's theorem. For each angular momentum $l$, introduction of quasiparticle operators yields coupled eigenvalue equations for the excited states; they can be expressed either in terms of Bogoliubov coherence amplitudes $u_l(r)$ and $v_l(r)$ that determine the appropriate linear combinations of particle operators, or in terms of hydrodynamic amplitudes $\rho_l'(r)$ and $\Phi_l'(r)$. The hydrodynamic picture suggests a simple variational approximation for $l >0$ that provides an upper bound for the lowest eigenvalue $\omega_l$ and an estimate for the corresponding zero-temperature occupation number $N_l'$; both expressions closely resemble those for a uniform bulk Bose condensate.Comment: 5 pages, RevTeX, contributed paper accepted for Low Temperature Conference, LT21, August, 199

Energy and Vorticity in Fast Rotating Bose-Einstein Condensates

We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by 1/\eps^2 and the rotational velocity by $\Omega$, we evaluate exactly the next to leading order contribution to the ground state energy in the parameter regime |\log\eps|\ll \Omega\ll 1/(\eps^2|\log\eps|) with \eps\to 0. While the TF energy includes only the contribution of the centrifugal forces the next order corresponds to a lattice of vortices whose density is proportional to the rotational velocity.Comment: 19 pages, LaTeX; typos corrected, clarifying remarks added, some rearrangements in the tex

Oscillations of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities, $\Omega$, where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency $\sqrt{6} \Omega$ in the rotating frame, irrespective of the mode multipolarity $m$, as well as a class of low energy modes with frequency proportional to $|m|/\Omega$. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.Comment: 4 pages, 2 figure

Effective bosonic hamiltonian for excitons : a too naive concept

Excitons, being made of two fermions, may appear from far as bosons. Their close-to-boson character is however quite tricky to handle properly. Using our commutation technique especially designed to deal with interacting close-to-boson particles, we here calculate the exact expansion in Coulomb interaction of theexciton-exciton correlations, and show that a naive effective bosonic hamiltonian for excitons cannot produce these X-X correlations correctly

An efficient method for the Quantum Monte Carlo evaluation of the static density-response function of a many-electron system

In a recent Letter we introduced Hellmann-Feynman operator sampling in diffusion Monte Carlo calculations. Here we derive, by evaluating the second derivative of the total energy, an efficient method for the calculation of the static density-response function of a many-electron system. Our analysis of the effect of the nodes suggests that correlation is described correctly and we find that the effect of the nodes can be dealt with

Thermal van der Waals Interaction between Graphene Layers

The van de Waals interaction between two graphene sheets is studied at finite temperatures. Graphene's thermal length $(\xi_T = \hbar v / k_B T)$ controls the force versus distance $(z)$ as a crossover from the zero temperature results for $z\ll \xi_T$, to a linear-in-temperature, universal regime for $z\gg \xi_T$. The large separation regime is shown to be a consequence of the classical behavior of graphene's plasmons at finite temperature. Retardation effects are largely irrelevant, both in the zero and finite temperature regimes. Thermal effects should be noticeable in the van de Waals interaction already for distances of tens of nanometers at room temperature.Comment: enlarged version, 9 pages, 4 figures, updated reference

An effective theory of Feshbach resonances and many-body properties of Fermi gases

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that for resonances in the fermionic systems $^{6}$Li and $^{40}$K that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.Comment: 4 pages, 1 figure, NORDITA-2003-21 C

Compressible quantum phases from conformal field theories in 2+1 dimensions

Conformal field theories (CFTs) with a globally conserved U(1) charge Q can be deformed into compressible phases by modifying their Hamiltonian, H, by a chemical potential H -> H - \mu Q. We study 2+1 dimensional CFTs upon which an explicit S duality mapping can be performed. We find that this construction leads naturally to compressible phases which are superfluids, solids, or non-Fermi liquids which are more appropriately called `Bose metals' in the present context. The Bose metal preserves all symmetries and has Fermi surfaces of gauge-charged fermions, even in cases where the parent CFT can be expressed solely by bosonic degrees of freedom. Monopole operators are identified as order parameters of the solid, and the product of their magnetic charge and Q determines the area of the unit cell. We discuss implications for holographic theories on asymptotically AdS4 spacetimes: S duality and monopole/dyon fields play important roles in this connection.Comment: 30 pages, 2 figures; (v2) small corrections and more ref

Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate

A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the circulating superfluid velocity far from the vortex core provides a small perturbation that splits the originally degenerate normal modes of a vortex-free condensate. The relative frequency shifts are small in all cases considered (they vanish for the lowest dipole mode with |m|=1), suggesting that the vortex is stable. The Bogoliubov equations serve to verify the existence of helical waves, similar to those of a vortex line in an unbounded weakly interacting Bose gas. In the large-condensate (small-core) limit, the condensate wave function reduces to that of a straight vortex in an unbounded condensate; the corresponding Bogoliubov equations have no bound-state solutions that are uniform along the symmetry axis and decay exponentially far from the vortex core.Comment: 15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We have altered the material in Secs. 3B and 4 in connection with the normal modes that have |m|=1. Our present treatment satisfies the condition that the fundamental dipole mode of a condensate with (or without) a vortex should have the bare frequency $\omega_\perp

An Active-Sterile Neutrino Transformation Solution for r-Process Nucleosynthesis

We discuss how matter-enhanced active-sterile neutrino transformation in both neutrino and antineutrino channels could enable the production of the rapid neutron capture (r-process) nuclei in neutrino-heated supernova ejecta. In this scheme the lightest sterile neutrino would be heavier than the electron neutrino and split from it by a vacuum mass-squared difference roughly between 3 and 70 eV$^2$ and vacuum mixing angle given by $\sin^2 2\theta_{es} > 10^{-4}$.Comment: 27 pages plus twelve figures. Submitted to Phys. Rev.