关于双Floquet-Bloch变换及针对周期结构的Green函数远场渐近性的注记

Discrete convolution operators in positive characteristic: a variation on the Floquet-Bloch Theory

The classical Floquet theory deals with Floquet-Bloch solutions of periodic PDEs (see e.g., P. Kuchment. Floquet Theory for Partial Differential Equations. Basel: Birkhauser, 1993). Peter Kuchment developed as well a discrete version of this theory for difference vector equations on lattices, including the Floquet theory on infinite periodic graphs. Here we propose a variation on this theory for matrix convolution operators acting on vector functions on lattices with values in a field of positive characteristic.

The Floquet-Bloch Transform and Scattering from Locally Perturbed Periodic Surfaces

We use the Floquet-Bloch transform to reduce variational formulations of surface scattering problems for the Helmholtz equation from periodic and locally perturbed periodic surfaces to equivalent variational problems formulated on bounded domains. To this end, we establish various mapping properties of that transform between suitable weighted Sobolev spaces on periodic strip-like domains and coupled families of quasiperiodic Sobolev spaces. Our analysis shows in particular that the decay of solutions to surface scattering problems from locally perturbed periodic surfaces is precisely character…

Approximate normal forms via Floquet-Bloch theory: Nehorosev stability for linear waves in quasiperiodic media

We study the long-time behavior of the Schr{ö}dinger flow in a heterogeneous potential $λ$V with small intensity 0<$λ$$\ll$1 (or alternatively at high frequencies). The main new ingredient, which we introduce in the general setting of a stationary ergodic potential, is an approximate stationary Floquet--Bloch theory that is used to put the perturbed Schr{ö}dinger operator into approximate normal form. We apply this approach to quasiperiodic potentials and establish a Nehoro{\v s}ev-type stability result. In particular, this ensures asymptotic ballistic transport up to a stretched exponential t…

周期底部上水波的Bloch-Floquet带隙

Bloch-Floquet band gaps for water waves over a periodic bottom

本文针对周期底部上的线性化水波问题，利用Dirichlet-Neumann算子的解析性建立Bloch-Floquet理论，证明谱由带和间隙组成，并给出带隙大小与位置的显式公式。

周期磁拟微分算子的Bloch-Floquet分解中的纤维算子

The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators

本文研究了具有周期磁势的周期磁拟微分算子的纤维算子结构，给出了其分布核的显式公式，并证明了纤维算子是环面拟微分算子。

Floquet哈密顿量的准能谱的近不变性

Near invariance of quasi-energy spectrum of Floquet Hamiltonians

研究Floquet哈密顿量的准能谱近不变性，通过分析单射算子的谱性质及有效动力学，揭示其在周期性系统中的行为特性。