Related papers: Multi-frequency averaging and uniform accuracy tow…
Dynamical mean-field theory is generalized to solve the nonequilibrium Keldysh boundary problem: a system is started in equilibrium at a temperature T=0.1, a uniform electric field is turned on at t=0, and the system is monitored as it…
In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…
Bloch equations give a quantum description of the coupling between an atom and a driving electric force. In this article, we address the asymptotics of these equations for high frequency electric fields, in a weakly coupled regime. We prove…
We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields,…
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly…
In this paper, we will study the Bloch transformed rough surface scattering problems, and propose a numerical method based on the Bloch transformed problems. Based on the mathematical theory of the scattering problems from locally perturbed…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion…
Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of…
In the continuous time random walk model, the time-fractional operator usually expresses an infinite waiting time probability density. Different from that usual setting, this work considers the tempered time-fractional operator, which…
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…
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…
In this paper, we will introduce a high order numerical method to solve the scattering problems with non-periodic incident fields and (locally perturbed) periodic surfaces. For the problems we are considering, the classical methods to treat…
The dynamics of atom-molecule conversion system subject to dephasing noises is studied in this paper. With the dephasing master equation and the mean-field theory, we drive a Bloch equation for the system, this equation is compared with the…
Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from…
We study a Schr{\"o}dinger equation modeling the dynamics of an electron in a crystal in the asymptotic regime of small wavelength comparable to the characteristic scale of the crystal. Using Floquet Bloch decomposition, we obtain a…
This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\varepsilon$. The small parameter $\varepsilon>0$ denotes the…
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…