相关论文: Toward the spectral zone control
We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. We illustrate our…
We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
A controllable energy method, which considers the undersampling issue of the transfer function and valid spectral energy of a source signal, is proposed to implement angular spectrum diffraction calculation in near and far fields. The…
Exotic forms of wave control have been emerging by engineering matter in space and time. In this framework, temporal photonic interfaces, i.e., abrupt changes in the electromagnetic properties of a material, have been shown to induce…
The spectrum of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their…
Recently, we have discovered a new concept of permanent wave resonance with potential spatial oscillations. This means the constant wave swinging frequency on the whole energy intervals of spectral forbidden zones destroying physical…
The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary…
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect…
This paper is concerned with the notions of admissibility, exact controllability, exact observability and regularity of linear systems in the Banach space setting. It is proved that admissible controllability, exact controllability,…
Predictability horizon properties of chaotic dynamical systems can be related to their spectral properties. It is shown, using this relationship, that the spectral properties of the leading large-scale climate daily indices indicate a…
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
We study the essential spectra of formally self-adjoint elliptic systems on doubly periodic planar domains perturbed by a semi-infinite periodic row of foreign inclusions. We show that the essential spectrum of the problem consists of the…