Dimerized and trimerized phases for spin-2 Bosons in a one-dimensional optical lattice

We study the phase diagram for spin-2 bosons loaded in a one-dimensional optical lattice. By using non-Abelian density matrix renormalization group (DMRG) method we identify three possible phases: ferromagnetic, dimerized, and trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate two methods for identifying the phases. The first method is based on the spin-spin correlation function while in the second method one observes the excitation gap as a dimerization or a trimerization superlattice is imposed. The advantage of the second method is that it can also be easily implemented in experiments. By using the scattering lengths in the literature we estimate that $^{83}$Rb, $^{23}$Na, and $^{87}$Rb be ferromagnetic, dimerized, and trimerized respectively.Comment: 4 pages, 3 figures. Add acknowledgemen

Bubble Growth in Superfluid 3-He: The Dynamics of the Curved A-B Interface

We study the hydrodynamics of the A-B interface with finite curvature. The interface tension is shown to enhance both the transition velocity and the amplitudes of second sound. In addition, the magnetic signals emitted by the growing bubble are calculated, and the interaction between many growing bubbles is considered.Comment: 20 pages, 3 figures, LaTeX, ITP-UH 11/9

Supercurrent tunneling between conventional and unconventional superconductors: A Ginzburg-Landau approach

We investigate the Josephson tunneling between a conventional and an unconventional superconductor via a Ginzburg-Landau theory. This approach allows us to write down the general form of the Josephson coupling between the two superconductors, and to see which terms are forbidden or allowed by spatial symmetries. The time-reversal symmetry is also considered. We discuss the current-phase relationships, magnetic, and ac effects if we just include this direct coupling to the unconventional superconductor. In addition we consider the Josephson coupling between two short-coherence-length superconductors, extending the work of Deutscher and Müller (DM) to a finite-current calculation. We find that the critical current is suppressed below the DM value due to the fact that the coupling between the two superconductors across the junction depends on the phase difference and hence the current itself. Finally we investigate the possibility of the proximity effect, in particular the possibility that the conventional-type pairing is induced and hence coexists with the unconventional pairing near the junction. This would give the dominant contribution to the tunneling current if the direct tunneling to the unconventional pairs are suppressed for some reason. We point out that there is no possibility of dissipationless tunneling above the transition temperature of the unconventional superconductor. Even in the case in which the unconventional superconductor is below its transition temperature, we find that, for the possibility of a dissipationless current, it is crucial to have a coupling between the induced s wave and the unconventional superconductor that depends on their phase difference, which allows the conversion of the supercurrent from one type to the other. The behavior of this current, in particular as a function of temperature, is discussed. We also discuss the magnetic and time-dependent effects of the junction in the presence of this proximity effect. We see that, while some of these remain unaffected, some, in particular the time-dependent processes, are affected in a rather nontrivial manner

Stationary Josephson effect in a weak-link between nonunitary triplet superconductors

A stationary Josephson effect in a weak-link between misorientated nonunitary triplet superconductors is investigated theoretically. The non-self-consistent quasiclassical Eilenberger equation for this system has been solved analytically. As an application of this analytical calculation, the current-phase diagrams are plotted for the junction between two nonunitary bipolar $f-$wave superconducting banks. A spontaneous current parallel to the interface between superconductors has been observed. Also, the effect of misorientation between crystals on the Josephson and spontaneous currents is studied. Such experimental investigations of the current-phase diagrams can be used to test the pairing symmetry in the above-mentioned superconductors.Comment: 6 pages and 6 figure

Symmetry and inert states of spin Bose Condensates

We construct the list of all possible inert states of spin Bose condensates for $S \le 4$. In doing so, we also obtain their symmetry properties. These results are applied to classify line defects of these spin condensates at zero magnetic field.Comment: an error in Sec III C correcte

Superfluid stability in BEC-BCS crossover

We consider a dilute atomic gas of two species of fermions with unequal concentrations under a Feshbach resonance. We find that the system can have distinct properties due to the unbound fermions. The uniform state is stable only when either (a) beyond a critical coupling strength, where it is a gapless superfluid, or (b) when the coupling strength is sufficiently weak, where it is a normal Fermi gas mixture. Phase transition(s) must therefore occur when the resonance is crossed.Comment: 4 pages, 4 figure

Comparing the reliability of networks by spectral analysis

We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erd\H{o}s-R\'enyi, and the Small-World networks.Comment: 7 pages, 3 figure

Energy Resolved Supercurrent between two superconductors

In this paper I study the energy resolved supercurrent of a junction consisting of a dirty normal metal between two superconductors. I also consider a cross geometry with two additional arms connecting the above mentioned junction with two normal reservoirs at equal and opposite voltages. The dependence of the supercurrent between the two superconductors on the applied voltages is studied.Comment: revtex, 7 pages, 8 figures. accepted by Phys. Rev.