Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials

The optical nonlocality in symmetric metal-dielectric multilayer metamaterials is theoretically and experimentally investigated with respect to transverse-magnetic-polarized incident light. A nonlocal effective medium theory is derived from the transfer-matrix method to determine the nonlocal effective permittivity depending on both the frequency and wave vector in a symmetric metal-dielectric multilayer stack. In contrast to the local effective medium theory, our proposed nonlocal effective medium theory can accurately predict measured incident angle-dependent reflection spectra from a fabricated multilayer stack and provide nonlocal dispersion relations. Moreover, the bulk plasmon polaritons with large wave vectors supported in the multilayer stack are also investigated with the nonlocal effective medium theory through the analysis of the dispersion relation and eigenmode.Comment: 21 pages, 7 figure

Numerical simulation of nonoptimal dynamic equilibrium models

In this paper we present a recursive method for the computation of dynamic competitive equilibria in models with heterogeneous agents and market frictions. This method is based on a convergent operator over an expanded set of state variables. The fixed point of this operator defines the set of all Markovian equilibria. We study approximation properties of the operator as well as the convergence of the moments of simulated sample paths. We apply our numerical algorithm to two growth models, an overlapping generations economy with money, and an asset pricing model with financial frictions.Econometric models

Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems

Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become phase-locked to its radiated phonon waves, hence the mobility of the chain may decrease as one increases the external force.Comment: 4 figures, to appear in Phys. Rev.

Inhomogeneous Quasi-stationary States in a Mean-field Model with Repulsive Cosine Interactions

The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial conditions. The object of this paper is to show in a detailed manner how these structures arise and to explain their stability. By a convenient canonical transformation we rewrite the Hamiltonian in such a way that fast and slow variables are singled out and the canonical coordinates of a collective mode are naturally introduced. If, initially, enough energy is put in this mode, its decay can be extremely slow. However, both analytical arguments and numerical simulations suggest that these structures eventually decay to the spatially uniform equilibrium state, although this can happen on impressively long time scales. Finally, we heuristically introduce a one-particle time dependent Hamiltonian that well reproduces most of the observed phenomenology.Comment: to be published in J. Phys.

Giant supercurrent states in a superconductor-InAs/GaSb-superconductor junction

Superconductivity in topological materials has attracted a great deal of interest in both electron physics and material sciences since the theoretical predictions that Majorana fermions can be realized in topological superconductors [1-4]. Topological superconductivity could be realized in a type II, band-inverted, InAs/GaSb quantum well if it is in proximity to a conventional superconductor. Here we report observations of the proximity effect induced giant supercurrent states in an InAs/GaSb bilayer system that is sandwiched between two superconducting tantalum electrodes to form a superconductor-InAs/GaSb-superconductor junction. Electron transport results show that the supercurrent states can be preserved in a surprisingly large temperature-magnetic field (T-H) parameter space. In addition, the evolution of differential resistance in T and H reveals an interesting superconducting gap structure

Geometric stabilization of extended S=2 vortices in two-dimensional photonic lattices: theoretical analysis, numerical computation and experimental results

In this work, we focus our studies on the subject of nonlinear discrete self-trapping of S=2 (doubly-charged) vortices in two-dimensional photonic lattices, including theoretical analysis, numerical computation and experimental demonstration. We revisit earlier findings about S=2 vortices with a discrete model, and find that S=2 vortices extended over eight lattice sites can indeed be stable (or only weakly unstable) under certain conditions, not only for the cubic nonlinearity previously used, but also for a saturable nonlinearity more relevant to our experiment with a biased photorefractive nonlinear crystal. We then use the discrete analysis as a guide towards numerically identifying stable (and unstable) vortex solutions in a more realistic continuum model with a periodic potential. Finally, we present our experimental observation of such geometrically extended S=2 vortex solitons in optically induced lattices under both self-focusing and self-defocusing nonlinearities, and show clearly that the S=2 vortex singularities are preserved during nonlinear propagation

Trends in Elasticity and Electronic Structure of Transition-Metal Nitrides and Carbides from First Principles

The elastic properties of the $B_1$-structured transition-metal nitrides and their carbide counterparts are studied using the {\it ab initio\} density functional perturbation theory. The linear response results of elastic constants are in excellent agreement with those obtained from numerical derivative methods, and are also consistent with measured data. We find the following trends: (1) Bulk moduli $B$ and tetragonal shear moduli $G^{\prime}=(C_{11}-C_{12})/2$, increase and lattice constants $a_{0}$ decrease rightward or downward on the Periodic Table for the metal component or if C is replaced by N; (2) The inequality $B > G^{\prime} > G > 0$ holds for $G=C_{44}$; (3) $G$ depends strongly on the number of valence electrons per unit cell ($Z_{V}$). From the fitted curve of $G$ as a function of $Z_{V}$, we can predict that MoN is unstable in $B_{1}$ structure, and transition-metal carbonitrides ($e.g.$ ZrC$_{x}$N$_{1-x}$) and di-transition-metal carbides ($e.g.$ Hf$_{x}$Ta$_{1-x}$C) have maximum $G$ at $Z_{V} \approx 8.3$.Comment: 4 pages, 2 figures, submitted to PRL. 2 typos in ref. 15 were correcte

Resonant steps and spatiotemporal dynamics in the damped dc-driven Frenkel-Kontorova chain

Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant external force are investigated. Resonant steplike transitions of the average velocity occur due to the competitions between the moving kinks and their radiated phasonlike modes. A mean-field consideration is introduced to give a precise prediction of the resonant steps. Slip-stick motion and spatiotemporal dynamics on those resonant steps are discussed. Our results can be applied to studies of the fluxon dynamics of 1D Josephson-junction arrays and ladders, dislocations, tribology and other fields.Comment: 20 Plain Latex pages, 10 Eps figures, to appear in Phys. Rev.

Soliton stripes in two-dimensional nonlinear photonic lattices

We study experimentally the interaction of a soliton with a nonlinear lattice. We observe the formation of a novel type of composite soliton created by strong coupling of mutually incoherent periodic and localized beam components. By imposing an initial transverse momentum on the soliton stripe, we observe the effect of lattice compression and deformation.Comment: three pages, four figure