Decay of superfluid currents in a moving system of strongly interacting bosons

We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.Accepted manuscrip

The Offset Filtration of Convex Objects

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested simplicial complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based on the Voronoi partition with respect to the given convex objects. The size of the filtration and the time complexity for computing it are proportional to the size of the Voronoi diagram and its time complexity, respectively. Our approach is inspired by alpha-complexes for point sets, but requires more involved machinery and analysis primarily since Voronoi regions of general convex objects do not form a good cover. We show by experiments that our approach results in a similarly fast and topologically more stable method for computing a filtration compared to approximating the input by a point sample

Decay of super-currents in condensates in optical lattices

In this paper we discuss decay of superfluid currents in boson lattice systems due to quantum tunneling and thermal activation mechanisms. We derive asymptotic expressions for the decay rate near the critical current in two regimes, deep in the superfluid phase and close to the superfluid-Mott insulator transition. The broadening of the transition at the critical current due to these decay mechanisms is more pronounced at lower dimensions. We also find that the crossover temperature below which quantum decay dominates is experimentally accessible in most cases. Finally, we discuss the dynamics of the current decay and point out the difference between low and high currents.Comment: Contribution to the special issue of Journal of Superconductivity in honor of Michael Tinkham's 75th birthda

Finite-size effects in tunneling between parallel quantum wires

We present theoretical calculations and experimental measurements which reveal finite-size effects in the tunneling between two parallel quantum wires, fabricated at the cleaved edge of a GaAs/AlGaAs bilayer heterostructure. Observed oscillations in the differential conductance, as a function of bias voltage and applied magnetic field, provide direct information on the shape of the confining potential. Superimposed modulations indicate the existence of two distinct excitation velocities, as expected from spin-charge separation.Comment: Accepted to Phys. Rev. Lett. 7/200

An alternative field theory for the Kosterlitz-Thouless transition

We extend a Gaussian model for the internal electrical potential of a two-dimensional Coulomb gas by a non-Gaussian measure term, which singles out the physically relevant configurations of the potential. The resulting Hamiltonian, expressed as a functional of the internal potential, has a surprising large-scale limit: The additional term simply counts the number of maxima and minima of the potential. The model allows for a transparent derivation of the divergence of the correlation length upon lowering the temperature down to the Kosterlitz-Thouless transition point.Comment: final version, extended discussion, appendix added, 8 pages, no figure, uses IOP documentclass iopar

Tunneling effect on composite fermion pairing state in bilayer quantum Hall system

We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at \nu=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.