Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\Omega$ to exceed the radial harmonic frequency $\omega_\perp$. In the regime $\Omega \gtrsim \omega_\perp$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity $\Omega_h$, a central hole appears in the condensate. Numerical studies confirm the predicted value of $\Omega_h$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).Comment: 14 pages, 5 figure

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

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.

The s-wave pion-nucleus optical potential

We calculate the s-wave part of the pion-nucleus optical potential using a unitarized chiral approach that has been previously used to simultaneously describe pionic hydrogen and deuterium data as well as low energy pi N scattering in the vacuum. This energy dependent model allows for additional isoscalar parts in the potential from multiple rescattering. We consider Pauli blocking and pion polarization in an asymmetric nuclear matter environment. Also, higher order corrections of the pi N amplitude are included. The model can accommodate the repulsion required by phenomenological fits, though the theoretical uncertainties are bigger than previously thought. At the same time, we also find an enhancement of the isovector part compatible with empirical determinations.Comment: 31 pages, 27 figure

Vortex line in a neutral finite-temperature superfluid Fermi gas

The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov-de Gennes theory. Various thermodynamic properties are calculated and the shift in the critical temperature due to the presence of the vortex is analyzed. The gapless excitations inside the vortex core are studied and a scheme to detect these states and thus the presence of the vortex is examined. The numerical results are compared with various analytical expressions when appropriate.Comment: 8 pages, 6 embedded figure

Electron-phonon coupling and phonon self-energy in MgB2_2: do we really understand MgB2_2 Raman spectra ?

We consider a model Hamiltonian fitted on the ab-initio band structure to describe the electron-phonon coupling between the electronic $\sigma-$bands and the phonon E$_{2g}$ mode in MgB$_2$. The model allows for analytical calculations and numerical treatments using very large k-point grids. We calculate the phonon self-energy of the E$_{2g}$ mode along two high symmetry directions in the Brillouin zone. We demonstrate that the contribution of the $\sigma$ bands to the Raman linewidth of the E$_{2g}$ mode via the electron-phonon coupling is zero. As a consequence the large resonance seen in Raman experiments cannot be interpreted as originated from the $E_{2g}$ mode at $\Gamma$. We examine in details the effects of Fermi surface singularities in the phonon spectrum and linewidth and we determine the magnitude of finite temperature effects in the the phonon self-energy. From our findings we suggest several possible effects which might be responsible for the MgB$_2$ Raman spectra.Comment: 10 pages, 9 figure

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

Conductivity of the classical two-dimensional electron gas

We discuss the applicability of the Boltzmann equation to the classical two-dimensional electron gas. We show that in the presence of both the electron-impurity and electron-electron scattering the Boltzmann equation can be inapplicable and the correct result for conductivity can be different from the one obtained from the kinetic equation by a logarithmically large factor.Comment: Revtex, 3 page