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

Thermodynamic properties of a dipolar Fermi gas

Based on the semi-classical theory, we investigate the thermodynamic properties of a dipolar Fermi gas. Through a self-consistent procedure, we numerically obtain the phase space distribution function at finite temperature. We show that the deformations in both momentum and real space becomes smaller and smaller as one increases the temperature. For homogeneous case, we also calculate pressure, entropy, and heat capacity. In particular, at low temperature limit and in weak interaction regime, we obtain an analytic expression for the entropy, which agrees qualitatively with our numerical result. The stability of a trapped gas at finite temperature is also explored

Quasiparticle and Optical Properties of Rutile and Anatase TiO2_{2}

Quasiparticle excitation energies and optical properties of TiO$_{2}$ in the rutile and anatase structures are calculated using many-body perturbation theory methods. Calculations are performed for a frozen crystal lattice; electron-phonon coupling is not explicitly considered. In the GW method, several approximations are compared and it is found that inclusion of the full frequency dependence as well as explicit treatment of the Ti semicore states are essential for accurate calculation of the quasiparticle energy band gap. The calculated quasiparticle energies are in good agreement with available photoemission and inverse photoemission experiments. The results of the GW calculations, together with the calculated static screened Coulomb interaction, are utilized in the Bethe-Salpeter equation to calculate the dielectric function $\epsilon_{2}(\omega)$ for both the rutile and anatase structures. The results are in good agreement with experimental observations, particularly the onset of the main absorption features around 4 eV. For comparison to low temperature optical absorption measurements that resolve individual excitonic transitions in rutile, the low-lying discrete excitonic energy levels are calculated with electronic screening only. The lowest energy exciton found in the energy gap of rutile has a binding energy of 0.13 eV. In agreement with experiment, it is not dipole allowed, but the calculated exciton energy exceeds that measured in absorption experiments by about 0.22 eV and the scale of the exciton binding energy is also too large. The quasiparticle energy alignment of rutile is calculated for non-polar (110) surfaces. In the GW approximation, the valence band maximum is 7.8 eV below the vacuum level, showing a small shift from density functional theory results.Comment: Submitted to Physical Review

Spin-dependent Hedin's equations

Hedin's equations for the electron self-energy and the vertex were originally derived for a many-electron system with Coulomb interaction. In recent years it has been increasingly recognized that spin interactions can play a major role in determining physical properties of systems such as nanoscale magnets or of interfaces and surfaces. We derive a generalized set of Hedin's equations for quantum many-body systems containing spin interactions, e.g. spin-orbit and spin-spin interactions. The corresponding spin-dependent GW approximation is constructed.Comment: 5 pages, 1 figur

Dynamical fermion mass generation by a strong Yukawa interaction

We consider a model with global Abelian chiral symmetry of two massless fermion fields interacting with a complex massive scalar field. We argue that the Schwinger-Dyson equations for the fermion and boson propagators admit ultraviolet-finite chiral-symmetry-breaking solutions provided the Yukawa couplings are large enough. The fermions acquire masses and the elementary excitations of the complex scalar field are the two real spin-zero particles with different masses. As a necessary consequence of the dynamical chiral symmetry breakdown both in the fermion and scalar sectors, one massless pseudoscalar Nambu--Goldstone boson appears in the spectrum as a collective excitation of both the fermion and the boson fields. Its effective couplings to the fermion and boson fields are calculable.Comment: 9 pages, REVTeX4, uses feynmp, 1 eps figur

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

Loss of superfluidity by fermions in the boson Hubbard model on an optical lattice

The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of the bosons to the higher Bloch bands, coupled with the contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss implications for cold atom experiments where the expansion of the Mott lobes by fermions has been conclusively established.Comment: 4 pages, 1 eps figure, minor change

Anomalous Pinning Fields in Helical Magnets: Screening of the Quasiparticle Interaction

The spin-orbit interaction strength g_so in helical magnets determines both the pitch wave number q and the critical field H_c1 where the helix aligns with an external magnetic field. Within a standard Landau-Ginzburg-Wilson (LGW) theory, a determination of g_so in MnSi and FeGe from these two observables yields values that differ by a factor of 20. This discrepancy is remedied by considering the fermionic theory underlying the LGW theory, and in particular the effects of screening on the effective electron-electron interaction that results from an exchange of helical fluctuations.Comment: 4pp, 2 fig

On the Quantum Kinetic Equation in Weak Turbulence

The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a perturbation expansion which places the large diagonal component of the quartic term in the unperturbed Hamiltonian. Although one is not perturbing around a free field theory, the calculation is easily tractable owing to the fact that the unperturbed Hamiltonian can be written solely in terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.

On the Cholesky Decomposition for electron propagator methods: General aspects and application on C60

To treat the electronic structure of large molecules by electron propagator methods we developed a parallel computer program called P-RICD$\Sigma$. The program exploits the sparsity of the two-electron integral matrix by using Cholesky decomposition techniques. The advantage of these techniques is that the error introduced is controlled only by one parameter which can be chosen as small as needed. We verify the tolerance of electron propagator methods to the Cholesky decomposition threshold and demonstrate the power of the P-RICD$\Sigma$ program for a representative example (C60). All decomposition schemes addressed in the literature are investigated. Even with moderate thresholds the maximal error encountered in the calculated electron affinities and ionization potentials amount to a few meV only, and the error becomes negligible for small thresholds.Comment: 30 pages, 6 figures submitted to J.Chem. Phy