Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non- Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and ex- plore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase tran- sition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops

Global existence for a translating near-circular Hele-Shaw bubble with surface tension

This paper concerns global existence for arbitrary nonzero surface tension of bubbles in a Hele-Shaw cell that translate in the presence of a pressure gradient. When the cell width to bubble size is sufficiently large, we show that a unique steady translating near-circular bubble symmetric about the channel centerline exists, where the bubble translation speed in the laboratory frame is found as part of the solution. We prove global existence for symmetric sufficiently smooth initial conditions close to this shape and show that the steady translating bubble solution is an attractor within this class of disturbances. In the absence of side walls, we prove stability of the steady translating circular bubble without restriction on symmetry of initial conditions. These results hold for any nonzero surface tension despite the fact that a local planar approximation near the front of the bubble would suggest Saffman Taylor instability. We exploit a boundary integral approach that is particularly suitable for analysis of nonzero viscosity ratio between fluid inside and outside the bubble. An important element of the proof was the introduction of a weighted Sobolev norm that accounts for stabilization due to advection of disturbances from the front to the back of the bubble

Relation between vibrotactile perception thresholds and reductions in finger blood flow induced by vibration of the hand at frequencies in the range 8–250 Hz

Purpose: this study investigated how the vasoconstriction induced by vibration depends on the frequency of vibration when the vibration magnitude is defined by individual thresholds for perceiving vibration [i.e. sensation levels (SL)].Methods: fourteen healthy subjects attended the laboratory on seven occasions: for six vibration frequencies (8, 16, 31.5, 63, 125, or 250 Hz) and a static control condition. Finger blood flow (FBF) was measured in the middle fingers of both hands at 30-second intervals during five successive periods: (i) no force or vibration, (ii) 2-N force, no vibration, (iii) 2-N force, vibration, (iv) 2-N force, no vibration, (v) no force or vibration. During period (iii), vibration was applied to the right thenar eminence via a 6-mm diameter probe during ten successive 3-min periods as the vibration magnitude increased in ten steps (?10 to +40 dB SL).Results: with vibration at 63, 125, and 250 Hz, there was vasoconstriction on both hands when the vibration magnitude reached 10 dB SL. With vibration at 8, 16, and 31.5 Hz, there was no significant vasoconstriction until the vibration reached 25 dB SL. At all frequencies, there was greater vasoconstriction with greater magnitudes of vibration.Conclusions: it is concluded that at the higher frequencies (63, 125, and 250 Hz), the Pacinian channel mediates vibrotactile sensations near threshold and vasoconstriction occurs when vibration is perceptible. At lower frequencies (8, 16, and 31.5 Hz), the Pacinian channel does not mediate sensations near threshold and vasoconstriction commences at greater magnitudes when the Pacinian channel is activate

Optimizing condition numbers

In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers

Complex Dynamics of Correlated Electrons in Molecular Double Ionization by an Ultrashort Intense Laser Pulse

With a semiclassical quasi-static model we achieve an insight into the complex dynamics of two correlated electrons under the combined influence of a two-center Coulomb potential and an intense laser field. The model calculation is able to reproduce experimental data of nitrogen molecules for a wide range of laser intensities from tunnelling to over-the-barrier regime, and predicts a significant alignment effect on the ratio of double over single ion yield. The classical trajectory analysis allows to unveil sub-cycle molecular double ionization dynamics.Comment: 5 pages, 5 figures. to appear in Phys. Rev. Lett.(2007