相关论文: First Bloch eigenvalue in high contrast media

In this work we present new wall-laws boundary conditions including microscopic oscillations. We consider a newtonian flow in domains with periodic rough boundaries that we simplify considering a Laplace operator with periodic inflow and…

We study the first Dirichlet eigenfunction of the Laplacian in a $n$-dimensional convex domain. For domains of a fixed inner radius, estimates of Chiti imply that the ratio of the $L^2$-norm and $L^{\infty}$-norm of the eigenfunction is…

Simultaneous measurements of position and momentum are considered in $n$ dimensions. We find, that for a particle whose position is strictly localized in a compact domain $D\subset \mathbb{R}^n$ (spatial uncertainty) with non-empty…

We analyze the validity of Eliashberg theory of phonon-mediated superconductivity in 2D systems in light of recent extensive Monte-Carlo studies of the Holstein model. Conventional wisdom says that Eliashberg theory is applicable as long as…

Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…

The interaction between a magnetic thin film and a superconductor is studied. In particular, the equilibrium width of a Bloch wall is estimated with and without the superconductor. It is shown that the Bloch wall experiences a small…

We theoretically show that the frequency and momentum of a photon are not necessarily proportional to one another at low frequencies in photonic crystals comprising materials with positive- and negative-valued material properties. We…

We calculate analytically properties of holographic superconductors in the probe limit. We analyze the range $1/2 < \Delta < 3$, where $\Delta$ is the dimension of the operator that condenses. We obtain the critical temperature in terms of…

We study $(1+1)$-dimensional p-wave holographic superconductors described by three dimensional Einstein-Maxwell gravity coupled to a massive complex vector field in the context of $AdS_3/CFT_2$ correspondence. In the probe limit where the…

Eigenvalues arising in scattering theory have been envisioned as a potential source of target signatures in nondestructive testing of materials, whereby perturbations of the eigenvalues computed for a penetrable medium would be used to…

The reflectance of high-quality, unpolished single crystals of YBa_2Cu_3O_{6+x}, for the doping range x=0.50 -> 0.95, has been measured with radiation polarized along the c axis from approx 50 cm^{-1} to 5000 cm^{-1} between 10 K and 300 K.…

In this paper we report the first experimental measurement of the infrared conductivity of ultra-thin quenched-condensed Pb films. For dc sheet resistances such that $\omega \tau \ll 1$ the ac conductance increases with frequency but is in…

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in…

We search for anomalous normal and superconductive behavior in the two-band Hubbard model with one narrow band. We analyze the influence of electron-polaron effect and Altshuler-Aronov effect on effective mass enhancement and scattering…

Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a…

In some linearly unstable flows, secondary instability is found to have a much larger wavelength than that of the primary unstable modes, so that it cannot be recovered with a classical Floquet analysis. In this work, we apply a new…

We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three- and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with…

We report on theoretical analysis of large amplitude current dynamics due to Bragg reflections in carbon nanotubes exposed to an external electric field. Using the kinetic equation with constant relaxation time, an analytical expression for…

We build an effective medium theory for two-dimensional photonic crystals comprising a rectangular lattice of dielectric cylinders with the incident electric field polarized along the axis of the cylinders. In particular, we discuss the…

We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit…