Edge States and Broken Symmetry Phases of Laterally Confined 3^3He Films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D) $^3$He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum, $L_z = (N/2) \hbar$, for $N/2$ Cooper pairs. The power law suppression of the angular momentum, $L_z(T) \simeq (N/2)\,\hbar\,[1 - \frac{2}{3}(\pi T/\Delta)^2 ]$ for $0 \le T \ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing surfaces on the edge currents, ground-state angular momentum and ground-state order parameter. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at $D_{c2} \approx 16 \xi_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length $D\rightarrow D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and orignates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral "polar phase" at $D_{c1} \approx 9\xi_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.Comment: 16 pages, 16 figure

Anisotropy and Strong-Coupling Effects on the Collective Mode Spectrum of Chiral Superconductors: Application to Sr2_2RuO4_4

Recent theories of Sr$_2$RuO$_4$ based on the interplay of strong interactions, spin-orbit coupling and multi-band anisotropy predict chiral or helical ground states with strong anisotropy of the pairing states, with deep minima in the excitation gap, as well as strong phase anisotropy for the chiral ground state. We develop time-dependent mean field theory to calculate the Bosonic spectrum for the class of 2D chiral superconductors spanning $^3$He-A to chiral superconductors with strong anisotropy. Chiral superconductors support a pair of massive Bosonic excitations of the time-reversed pairs labeled by their parity under charge conjugation. These modes are degenerate for 2D $^3$He-A. Crystal field anisotropy lifts the degeneracy. Strong anisotropy also leads to low-lying Fermions, and thus to channels for the decay of the Bosonic modes. Selection rules and phase space considerations lead to large asymmetries in the lifetimes and hybridization of the Bosonic modes with the continuum of un-bound Fermion pairs. We also highlight results for the excitation of the Bosonic modes by microwave radiation that provide clear signatures of the Bosonic modes of an anisotropic chiral ground state.Comment: 11 pages with 8 figures. Presented as an invited talk as SCES14, Grenoble, France, July 201

Cosmological dynamics of scalar fields with O(N) symmetry

In this paper, we study the cosmological dynamics of scalar fields with O(N) symmetry in general potentials. We compare the phase space of the dynamical systems of the quintessence and phantom and give the conditions for the existence of various attractors as well as their cosmological implications. We also show that the existence of tracking attractor in O(N) phantom models require the potential with $\Gamma<1/2$, which makes the models with exponential potential possess no tracking attractor.Comment: 9 pages, 4 figures; Replaced with the version to be published in Classical and Quantum Gravity. Reference adde

Microscopic Theory of Spontaneous Decay in a Dielectric

The local field correction to the spontanous dacay rate of an impurity source atom imbedded in a disordered dielectric is calculated to second order in the dielectric density. The result is found to differ from predictions associated with both "virtual" and "real" cavity models of this decay process. However, if the contributions from two dielectric atoms at the same position are included, the virtual cavity result is reproduced.Comment: 12 Page

Large-eddy simulations of high Reynolds number jets with a suitable subgrid-scale model for solver dependency study

Large-eddy simulations are performed of a turbulent round jet at Ma = 0.5 and 0.9. The solver dependency is explored on computationally affordable grids of 5 and 20 million grid points, by taking advantage of the consistency of the subgrid-scale sigma-model. Three different solvers are tested. With all three, the computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements, for both Mach numbers and both grids, showing the strength of the sigma-model in adapting to different flow conditions and grid refinements

Sub-wavelength imaging at optical frequencies using canalization regime

Imaging with sub-wavelength resolution using a lens formed by periodic metal-dielectric layered structure is demonstrated. The lens operates in canalization regime as a transmission device and it does not involve negative refraction and amplification of evanescent modes. The thickness of the lens have to be an integer number of half-wavelengths and can be made as large as required for ceratin applications, in contrast to the other sub-wavelength lenses formed by metallic slabs which have to be much smaller than the wavelength. Resolution of $\lambda/20$ at 600 nm wavelength is confirmed by numerical simulation for a 300 nm thick structure formed by a periodic stack of 10 nm layers of glass with $\epsilon=2$ and 5 nm layers of metal-dielectric composite with $\epsilon=-1$. Resolution of $\lambda/60$ is predicted for a structure with same thickness, period and operating frequency, but formed by 7.76 nm layers of silicon with $\epsilon=15$ and 7.24 nm layers of silver with $\epsilon=-14$.Comment: 4 pages, 4 figures, submitted to PR

Internal Josephson-Like Tunneling in Two-Component Bose-Einstein Condensates Affected by Sign of the Atomic Interaction and External Trapping Potential

We study the Josephson-like tunneling in two-component Bose-Einstein condensates coupled with microwave field in respond to various attractive and repulsive atomic interaction under the various aspect ratio of trapping potential and the gravitational field. It is very interesting to find that the dynamic of Josephson-like tunneling can be controlled from fast damped oscillations and asymmetric occupation to nondamped oscillation and symmetric occupation.Comment: 4 pages, 5 figure

Bulge formation from SSCs in a responding cuspy dark matter halo

We simulate the bulge formation in very late-type dwarf galaxies from circumnuclear super star clusters (SSCs) moving in a responding cuspy dark matter halo (DMH). The simulations show that (1) the response of DMH to sinking of SSCs is detectable only in the region interior to about 200 pc. The mean logarithmic slope of the responding DM density profile over that area displays two different phases: the very early descent followed by ascent till approaching to 1.2 at the age of 2 Gyrs. (2) the detectable feedbacks of the DMH response on the bulge formation turned out to be very small, in the sense that the formed bulges and their paired nuclear cusps in the fixed and the responding DMH are basically the same, both are consistent with $HST$ observations. (3) the yielded mass correlation of bulges to their nuclear (stellar) cusps and the time evolution of cusps' mass are accordance with recent findings on relevant relations. In combination with the consistent effective radii of nuclear cusps with observed quantities of nuclear clusters, we believe that the bulge formation scenario that we proposed could be a very promising mechanism to form nuclear clusters.Comment: 27 pages, 11 figures, accepted for publication in Ap