Vortex Ring Dynamics in Trapped Bose-Einstein Condensates

We use the time-dependent Gross-Pitaevskii equation to study the motion of a vortex ring produced by phase imprinting on an elongated cloud of cold atoms. Our approach models the experiments of Yefsah et. al. [Nature \textbf{499}, 426] on $^6$Li in the BEC regime where the fermions are tightly bound into bosonic dimers. We find ring oscillation periods which are much larger than the period of the axial harmonic trap. Our results lend further strength to Bulgac et. al.'s arguments [arXiv: 1306.4266] that the "heavy solitons" seen in those experiments are actually vortex rings. We numerically calculate the periods of oscillation for the vortex rings as a function of interaction strength, trap aspect ratio, and minimum vortex ring radius. In the presence of axial anisotropies the rings undergo complicated internal dynamics where they break into sets of vortex lines, then later combine into rings. These structures oscillate with a similar frequency to simple axially symmetric rings.Comment: 6 pages, 6 figures, revtex4; new subsection and figure addressing axial asymmetry, added references to sections 2 and 3, minor changes to section 5, main conclusions unchange

Scaling behavior in a quantum wire with scatterers

We study the conductance properties of a straight two-dimensional quantum wire with impurities modeled by $s$-like scatterers. Their presence can lead to strong inter-channel coupling. It was shown that such systems depend sensitively on the number of transverse modes included. Based on a poor man's scaling technique we include the effect of higher modes in a renormalized coupling constant. We therefore show that the low-energy behavior of the wire is dominated by only a few modes, which hence is a way to reduce the necessary computing power. The technique is successfully applied to the case of one and two $s$-like scatterers.Comment: 7 pages, 7 figures included; to be published in Phys. Rev.

Symmetry in Critical Random Boolean Network Dynamics

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems

Relaxation Of Brownian Particles In A Gravitational Field

We describe an upper level undergraduate experiment on the time-dependent behavior of a suspension of Brownian particles under gravitational attraction. We employed the Fokker-Planck equation in the strong friction limit and measured the time-evolution of the probability distribution for 1.0 mu m diameter latex Brownian particles in water at room temperature and pressure. The experiment provides evidence of the atomic nature of water.Physic

Shear band formation in granular media as a variational problem

Strain in sheared dense granular material is often localized in a narrow region called shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The non-trivial shape of the shear band was measured as the function of the cell geometry. First we present a geometric argument for narrow shear bands which connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands which are detached from the free surface and are entirely covered in the bulk.Comment: 4 pages, 5 figures; minor changes, typos and journal-ref adde

Phase Diagram for a 2-D Two-Temperature Diffusive XY Model

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow through the system from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin-wave order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium the KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent of phi = 2.52 \pm 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.Comment: 5 pages, 4 figure

Transport coefficients from the Boson Uehling-Uhlenbeck Equation

We derive microscopic expressions for the bulk viscosity, shear viscosity and thermal conductivity of a quantum degenerate Bose gas above $T_C$, the critical temperature for Bose-Einstein condensation. The gas interacts via a contact potential and is described by the Uehling-Uhlenbeck equation. To derive the transport coefficients, we use Rayleigh-Schrodinger perturbation theory rather than the Chapman-Enskog approach. This approach illuminates the link between transport coefficients and eigenvalues of the collision operator. We find that a method of summing the second order contributions using the fact that the relaxation rates have a known limit improves the accuracy of the computations. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity remains identically zero as it is for the classical case.Comment: 10 pages, 2 figures, submitted to Phys. Rev.