相关论文: Toward the spectral zone control

We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…

It is shown that the interplay of a confining potential with a periodic potential leads for free particles to states spatially confined on a fraction of the total extension of the system. A more complex `slicing' of the system can be…

The eigenvalue spectrum of the adjacency matrix of a network is closely related to the behavior of many dynamical processes run over the network. In the field of robotics, this spectrum has important implications in many problems that…

A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…

Along with the scaling of dimensions in quantum systems, transitions between the system's energy levels would become close in frequency, which are conventionally resolved by weak and lengthy pulses. Here, we extend and experimentally…

We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…

Periodic optical structures, such as diffraction grating and numerous photonic crystals, are one of the staples of modern nanophotonics for the manipulation of electromagnetic radiation. The array of subwavelength dielectric rods is one of…

A key quantity that occurs in the error analysis of several numerical methods for eigenvalue problems is the distance between the eigenvalue of interest and the next nearest eigenvalue. When we are interested in the smallest or fundamental…

We study the long-time behaviour of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions…

We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed by Remling and the Boundary Control method. We show that…

We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…

The manipulation and movement of Dirac points in the Brillouin zone by the electron-electron interaction is considered within leading order perturbation theory. At the merging point, an infinitesimal interaction is shown to cause opening of…

We derive a systematic perturbative expansion for the finite-volume energy spectrum of the non-linear $O(N)$ $\sigma$-model in the $\delta$-regime. The violation of the power-counting rules that emerges after the separation of the fast and…

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned…

Recent years have witnessed a wave of research activities in systems science toward the study of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies in life and physical…

We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feasible region}. We show that this feasible region is a…

A variant of the complex Ginzburg-Landau equation is used to investigate the frequency locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, $\pi$ fronts,…

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…