Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate

We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center of mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in details and various regimes (van der Waals-London, Casimir-Polder and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for the case of a sapphire dielectric substrate interacting with a harmonically trapped condensate of $^{87}$Rb atoms. We find that at distances of $4-8 \mu m$, where thermal effects become visible, the relative frequency shifts produced by the substrate are of the order $10^{-4}$ and hence accessible experimentally. The effects of non linearities due to the finite amplitude of the oscillation are explicitly discussed. Predictions are also given for the radial breathing mode.Comment: 28 pages, 10 figures. Submitted to PR

A chiral crystal in cold QCD matter at intermediate densities?

The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q$) is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q$=0). The calculations are based on effective nonperturbative four-fermion interactions acting in both the scalar diquark as well as the scalar-isoscalar quark-hole ('$\sigma$') channel. Within the Nambu-Gorkov formalism we set up the coupled channel problem including multiple chiral density wave formation, and evaluate the resulting gaps and free energies. Employing medium-modified instanton-induced 't Hooft interactions, as applicable around $\mu_q\simeq 0.4$ GeV (or 4 times nuclear saturation density), we find the 'chiral crystal phase' to be competitive with the color superconductor.Comment: 14 pages ReVTeX, including 11 ps-/eps-figure

Strongly nonlinear dynamics of electrolytes in large ac voltages

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.Comment: 30 pages, 17 eps-figures, RevTe

Revised Phase Diagram of the Gross-Neveu Model

We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.Comment: Revtex, 12 pages, 15 figures; v2: Axis labelling in Fig. 9 correcte

Spontaneous symmetry breaking in strong-coupling lattice QCD at high density

We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find that the global symmetry of the ground state varies with N_f and with the background baryon density. In all cases the condensate breaks the discrete rotational symmetry of the lattice as well as part of the chiral symmetry group.Comment: 10 pages, RevTeX 4; added discussion of accidental degeneracy of vacuum after Eq. (35

Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities

We study the possibility of spatially non-uniform ground state in (1+1)-dimensional models with quartic fermi interactions at finite fermion densities by introducing chemical potential \mu. We examine the chiral Gross-Neveu model and the Cooper pair model as toy models of the chiral symmetry breaking and the difermion pair condensates which are presumed to exist in QCD. We confirm in the chiral Gross-Neveu model that the ground state has a crystalline structure in which the chiral condensate oscillates in space with wave number 2\mu. Whereas in the Cooper pair model we find that the vacuum structure is spatially uniform. Some discussions are given to explain this difference.Comment: 18 pages, REVTeX, 3 eps figure

Primordial Hypermagnetic Knots

Topologically non-trivial configurations of the hypermagnetic flux lines lead to the formation of hypermagnetic knots (HK) whose decay might seed the Baryon Asymmetry of the Universe (BAU).HK can be dynamically generated provided a topologically trivial (i.e. stochastic) distribution of flux lines is already present in the symmetric phase of the electroweak (EW) theory. In spite of the mechanism generating the HK, their typical size must exceed the diffusivity length scale. In the minimal standard model (MSM) (but not necessarily in its supersymmetric extension) HK are washed out. A classical hypermagnetic background in the symmetric phase of the EW theory can produce interesting amounts of gravitational radiation.Comment: 4 pages in Revtex style, 2 figure