Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry

We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these particle-hole symmetric systems the topological phases are characterized by an even-numbered winding number $\nu$. At a two-dimensional (2D) surface the topological properties of this quantum state manifest themselves through the presence of $\nu$ flavors of gapless Dirac fermion surface states, which are robust against localization from random impurities. We construct a tight-binding model on the diamond lattice that realizes a topologically nontrivial phase, in which the winding number takes the value $\nu =\pm 2$. Disorder corresponds to a (non-localizing) random SU(2) gauge potential for the surface Dirac fermions, leading to a power-law density of states $\rho(\epsilon) \sim \epsilon^{1/7}$. The bulk effective field theory is proposed to be the (3+1) dimensional SU(2) Yang-Mills theory with a theta-term at $\theta=\pi$.Comment: 5 pages, 3 figure

Observation of a 2D Bose-gas: from thermal to quasi-condensate to superfluid

We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz and Thouless (BKT) transition temperature. By measuring the density profile, \textit{in situ} and after time of flight, and the coherence length, we identify different states of the gas. In particular, we observe that the gas develops a bimodal distribution without long range order. In this state, the gas presents a longer coherence length than the thermal cloud; it is quasi-condensed but is not superfluid. Experimental evidence indicates that we observe the superfluid transition (BKT transition).Comment: 5 pages, 6 figure

Thermotaxis in Caenorhabditis elegans analyzed by measuring responses to defined thermal stimuli

In a spatial thermal gradient, Caenorhabditis elegans migrates toward and then isothermally tracks near its cultivation temperature. A current model for thermotactic behavior involves a thermophilic drive (involving the neurons AFD and AIY) and cryophilic drive (involving the neuron AIZ) that balance at the cultivation temperature. Here, we analyze the movements of individual worms responding to defined thermal gradients. We found evidence for a mechanism for migration down thermal gradients that is active at temperatures above the cultivation temperature, and a mechanism for isothermal tracking that is active near the cultivation temperature. However, we found no evidence for a mechanism for migration up thermal gradients at temperatures below the cultivation temperature that might have supported the model of opposing drives. The mechanisms for migration down gradients and isothermal tracking control the worm's movements in different manners. Migration down gradients works by shortening (lengthening) the duration of forward movement in response to positive (negative) temperature changes. Isothermal tracking works by orienting persistent forward movement to offset temperature changes. We believe preference for the cultivation temperature is not at the balance between two drives. Instead, the worm activates the mechanism for isothermal tracking near the cultivation temperature and inactivates the mechanism for migration down gradients near or below the cultivation temperature. Inactivation of the mechanism for migration down gradients near or below the cultivation temperature requires the neurons AFD and AIY

The MHD Kelvin-Helmholtz Instability II: The Roles of Weak and Oblique Fields in Planar Flows

We have carried out high resolution MHD simulations of the nonlinear evolution of Kelvin-Helmholtz unstable flows in 2 1/2 dimensions. The modeled flows and fields were initially uniform except for a thin shear layer with a hyperbolic tangent velocity profile and a small, normal mode perturbation. The calculations consider periodic sections of flows containing magnetic fields parallel to the shear layer, but projecting over a full range of angles with respect to the flow vectors. They are intended as preparation for fully 3D calculations and to address two specific questions raised in earlier work: 1) What role, if any, does the orientation of the field play in nonlinear evolution of the MHD Kelvin-Helmholtz instability in 2 1/2 D. 2) Given that the field is too weak to stabilize against a linear perturbation of the flow, how does the nonlinear evolution of the instability depend on strength of the field. The magnetic field component in the third direction contributes only through minor pressure contributions, so the flows are essentially 2D. Even a very weak field can significantly enhance the rate of energy dissipation. In all of the cases we studied magnetic field amplification by stretching in the vortex is limited by tearing mode, ``fast'' reconnection events that isolate and then destroy magnetic flux islands within the vortex and relax the fields outside the vortex. If the magnetic tension developed prior to reconnection is comparable to Reynolds stresses in the flow, that flow is reorganized during reconnection. Otherwise, the primary influence on the plasma is generation of entropy. The effective expulsion of flux from the vortex is very similar to that shown by Weiss for passive fields in idealized vortices with large magnetic Reynolds numbers. We demonstrated that thisComment: 23 pages of ApJ Latex (aaspp4.sty) with 10 figures, high resolution postscript images for figs 4-9 available through anonymous at ftp://ftp.msi.umn.edu/pub/twj To appear in the June 10, 1997 Ap

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Singular Density of States of Disordered Dirac Fermions in the Chiral Models

The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random chiral models. Two distinct structures of density of states (DoS) around zero energy, one is a power-law dependence on energy in the intermediate energy range and the other is a diverging one at zero energy, are revealed by an extensive numerical study for large systems up to $250\times 250$. For the random hopping model, our finding of the diverging DoS within very narrow energy range reconciles previous inconsistencies between the lattice and the continuum models.Comment: 4 pages, 4 figure