Size dependence of second-order hyperpolarizability of finite periodic chain under Su-Schrieffer-Heeger model

The second hyperpolarizability $\gamma_N(-3\omega\omega,\omega,\omega)$ of $N$ double-bond finite chain of trans-polyactylene is analyzed using the Su-Schrieffer-Heeger model to explain qualitative features of the size-dependence behavior of $\gamma_N$. Our study shows that $\gamma_N/N$ is {\it nonmonotonic} with $N$ and that the nonmonotonicity is caused by the dominant contribution of the intraband transition to $\gamma_N$ in polyenes. Several important physical effects are discussed to reduce quantitative discrepancies between experimental and our resultsComment: 3 figures, 1 tabl

Expanded mixed multiscale finite element methods and their applications for flows in porous media

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity and Lagrange multipliers. We use multiscale basis functions for the both velocity and gradient of pressure. In the expanded mixed MsFEM framework, we consider both cases of separable-scale and non-separable spatial scales. We specifically analyze the methods in three categories: periodic separable scales, $G$- convergence separable scales, and continuum scales. When there is no scale separation, using some global information can improve accuracy for the expanded mixed MsFEMs. We present rigorous convergence analysis for expanded mixed MsFEMs. The analysis includes both conforming and nonconforming expanded mixed MsFEM. Numerical results are presented for various multiscale models and flows in porous media with shales to illustrate the efficiency of the expanded mixed MsFEMs.Comment: 33 page

Thermal rectification in asymmetric U-shaped graphene flakes

In this paper, we study the thermal rectification in asymmetric U-shaped graphene flakes by using nonequilibrium molecular dynamics simulations. The graphene flakes are composed by a beam and two arms. It is found that the heat flux runs preferentially from the wide arm to the narrow arm which indicates a strong rectification effect. The dependence of the rectification ratio upon the heat flux, the length and the width of the beam, the length and width of the two arms are studied. The result suggests a possible route to manage heat dissipation in U-shaped graphene based nanoelectronic devices.Comment: 3 pages, 4 figure

Semiclassical Time Evolution of the Holes from Luttinger Hamiltonian

We study the semi-classical motion of holes by exact numerical solution of the Luttinger model. The trajectories obtained for the heavy and light holes agree well with the higher order corrections to the abelian and the non-abelian adiabatic theories in Ref. [1] [S. Murakami et al., Science 301, 1378(2003)], respectively. It is found that the hole trajectories contain rapid oscillations reminiscent of the "Zitterbewegung" of relativistic electrons. We also comment on the non-conservation of helicity of the light holes.Comment: 4 pages, 5 fugure

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde