Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions

We study asymptotic behaviour at time infinity of solutions close to the non-zero constant equilibrium for the Gross-Pitaevskii equation in two and three spatial dimensions. We construct a class of global solutions with prescribed dispersive asymptotic behavior, which is given in terms of the linearized evolution

Phonon-mediated tuning of instabilities in the Hubbard model at half-filling

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous electron-electron repulsion and electron-phonon interaction leads to new phases. In particular, a d$_{x^2-y^2}$-wave superconducting phase emerges when both anisotropic phonons and repulsive Hubbard interaction are present. For large electron-phonon couplings, charge-density-wave and s-wave superconducting regions also appear in the phase diagram, and the widths of these regions are strongly dependent on the phonon frequency, indicating that retardation effects play an important role. Since at half-filling the Fermi surface is nested, spin-density-wave is recovered when the repulsive interaction dominates. We employ a functional multiscale renormalization-group method that includes both electron-electron and electron-phonon interactions, and take retardation effects fully into account.Comment: 8 pages, 5 figure

Investigation of radar backscattering from second-year sea ice

The scattering properties of second-year ice were studied in an experiment at Mould Bay in April 1983. Radar backscattering measurements were made at frequencies of 5.2, 9.6, 13.6, and 16.6 GHz for vertical polarization, horizontal polarization and cross polarizations, with incidence angles ranging from 15 to 70 deg. The results indicate that the second-year ice scattering characteristics were different from first-year ice and also different from multiyear ice. The fading properties of radar signals were studied and compared with experimental data. The influence of snow cover on sea ice can be evaluated by accounting for the increase in the number of independent samples from snow volume with respect to that for bare ice surface. A technique for calculating the snow depth was established by this principle and a reasonable agreement has been observed. It appears that this is a usable way to measure depth in snow or other snow-like media using radar

Dynamical Properties of a Growing Surface on a Random Substrate

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force $F$ and temperature $T$. A continuous transition is found from high-temperature phase characterized by linear response to a low-temperature phase with nonlinear, temperature dependent response. In the simulated regime of driving force the numerical results are in general agreement with recent dynamic renormalization group predictions.Comment: 10 pages, latex, 3 figures, to appear in Phys. Rev. E (RC

Exotic Superconducting Phases of Ultracold Atom Mixtures on Triangular Lattices

We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in Phys. Rev. Lett. {\bf 97}, 030601 (2006). Using functional renormalization group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1/2 fermions on an isotropic lattice we find a competition of $s$-, $p$-, extended $d$-, and $f$-wave symmetry, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between $p$- and $f$-wave symmetry. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.Comment: 6 pages, 4 figures, extended version, slight modification

Stable directions for small nonlinear Dirac standing waves

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues close enough, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schr\"{o}dinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page

Unconventional Spin Density Waves in Dipolar Fermi Gases

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.Comment: 5 pages, 3 figure

TagF-mediated repression of bacterial type VI secretion systems involves a direct interaction with the cytoplasmic protein Fha

The bacterial type VI secretion system (T6SS) delivers effectors into eukaryotic host cells or toxins into bacterial competitor for survival and fitness. The T6SS is positively regulated by the threonine phosphorylation pathway (TPP) and negatively by the T6SS-accessory protein TagF. Here, we studied the mechanisms underlying TagF-mediated T6SS repression in two distinct bacterial pathogens, Agrobacterium tumefaciens and Pseudomonas aeruginosa. We found that in A. tumefaciens, T6SS toxin secretion and T6SS-dependent antibacterial activity are suppressed by a two-domain chimeric protein consisting of TagF and PppA, a putative phosphatase. Remarkably, this TagF domain is sufficient to post-translationally repress the T6SS, and this inhibition is independent of TPP. This repression requires interaction with a cytoplasmic protein, Fha, critical for activating T6SS assembly. In P. aeruginosa, PppA and TagF are two distinct proteins that repress T6SS in a TPP-dependent and -independent pathways, respectively. P. aeruginosa TagF interacts with Fha1, suggesting that formation of this complex represents a conserved TagF-mediated regulatory mechanism. Using TagF variants with substitutions of conserved amino acid residues at predicted protein-protein interaction interfaces, we uncovered evidence that the TagF-Fha interaction is critical for TagF-mediated T6SS repression in both bacteria. TagF inhibits T6SS without affecting T6SS protein abundance in A. tumefaciens, but TagF overexpression reduces the protein levels of all analyzed T6SS components in P. aeruginosa. Our results indicate that TagF interacts with Fha, which in turn could impact different stages of T6SS assembly in different bacteria, possibly reflecting an evolutionary divergence in T6SS control