Related papers: Gap opening in two-dimensional periodic systems
We show topological configurations of the complex-valued spectra in gapped non-Hermitian systems. These arise when the distinctive EPs in the energy Riemann sheets of such models are annihilated after threading them across the boundary of…
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger…
We present a tight-binding investigation of strained bilayer graphene within linear elasticity theory, focusing on the different environments experienced by the A and B carbon atoms of the different sublattices. We find that the…
For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…
We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…
Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…
The purpose of this article is the investigation of the global control properties of a coupled nonlinear dispersive system posed in the periodic domain $\mathbb{T}$, a system with the structure of a nonlinear Schr\"odinger equation and a…
We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space $L_2(\R^m)$, for $m \ge 2$. We specifically consider situations where high contrast in the coefficients leads to…
This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping.…
I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the…
Gapless spectrum of graphene allows easy spatial separation of electrons and holes with an external in-plane electric field. Guided collective plasmon modes can propagate along the separation line, whose amplitude decays with the distance…
We theoretically studied the interface states of liquid surface waves propagating through the heterojunctions formed by a bottom with one-dimensional periodic undulations. Via considering the periodic structure as a homogeneous one, our…
We consider Schr\"odinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
A phoxonic crystal waveguide with the glide symmetry is designed, in which both electromagnetic and elastic waves can propagate along the glide plane at the same time. Due to the band-sticking effect, super-cell bands of the waveguide…
We present some computer assisted methods to prove the existence of spectral gaps for the Almost Mathieu operator at critical coupling and give rigorous numerical estimates on their size. As an example we show that the first 8 gaps…
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
We report on existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. Zigzag quasi-one-dimensional configuration of waveguide array introduces strong…
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation…