Related papers: Floquet theory and stability for Hamiltonian parti…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
We examine the existence and uniqueness of invariant measures of a class of stochastic partial differential equations with Gaussian and Poissonian noise and its exponential convergence. This class especially includes a case of stochastic…
In (1+1)-dimensional quantum field theory, integrability is typically defined as the existence of an infinite number of local charges of different Lorentz spin, which commute with the Hamiltonian. A well known consequence of integrability…
Periodic eigendecomposition, to be formulated in this paper, is a numerical method to compute Floquet spectrum and Floquet vectors along periodic orbits in a dynamical system. It is rooted in numerical algorithms advances in computation of…
We develop a numerical method based on canonical conformal variables to study two eigenvalue problems for operators fundamental to finding a Stokes wave and its stability in a 2D ideal fluid with a free surface in infinite depth. We…
We study the effect of time-periodically varying the hopping amplitude in a one-dimensional Bose-Hubbard model, such that its time-averaged value is zero. Employing Floquet theory, we derive a static effective Hamiltonian in which…
We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high frequency regime. First, we consider a driving protocol relevant for experiments…
In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of obtaining a static effective Hamiltonian.…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown…
We consider the existence and spectral stability of periodic multi-pulse solutions in Hamiltonian systems which are translation invariant and reversible, for which the fifth-order Korteweg-de Vries equation is a prototypical example. We use…
Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
We introduce a new approach to the study of modulation of high-frequency periodic wave patterns, based on pseudodifferential analysis, multi-scale expansion, and Kreiss symmetrizer estimates like those in hyperbolic and hyperbolic-parabolic…
We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such configuration represents a line defect,…
This paper is concerned with difficulties encountered by engineers when they attempt to predict the orientation of fibers in the creation of injection molded plastic parts. It is known that Jeffery's equation, which was designed to model a…
Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here…
We study the localization-delocalization transition of Floquet eigenstates in a driven fermionic chain with an incommensurate Aubry-Andr\'{e} potential and a hopping amplitude which is varied periodically in time. Our analysis shows the…
We investigate the dynamical characterization theory for periodically driven systems in which Floquet topology can be fully detected by emergent topological patterns of quench dynamics in momentum subspaces called band-inversion surfaces.…
This thesis applies Floquet theory to analyze linear periodic time-varying (LPTV) systems, represented by a system of ordinary differential equations (ODEs) that depend on a time variable t and have a matrix of coefficients with period T>0.…