Related papers: Bloch-like waves in random-walk potentials based o…
The emerging possibilities to steer and control electronic motion on subcycle time scales with strong electric fields enable studying the nonperturbative optical response and Bloch bands' topological properties, originated from Berry's…
Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…
Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable…
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit…
The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of…
Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Central to this approach is the identification and utilization…
The behavior of a Bloch particle in a complex crystal with PT symmetry subjected to a sinusoidal ac force is theoretically investigated. For unbroken PT symmetry and in the single-band approximation, it is shown that time reversal symmetry…
The complex physics of self-assembly in colloidal crystals on deformable interfaces and surfaces poses interesting possibilities for the designability and synthesis of next-generation metamaterials. The goal of this article is to…
Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…
We study the emergence of quasiperiodic Bloch wave functions in quasicrystals, employing the one-dimensional Fibonacci model as a test case. We find that despite the fact that Bloch functions are not eigenfunctions themselves,…
It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of…
We study a Helmholtz-type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a two-dimensional periodic medium. The defect is…
The connection between symmetries and conservation laws is a cornerstone of physics. It underlies Bloch's theorem which explains wave phenomena in all linear periodic systems. Here we demonstrate that, in a nonlinear grating with memory,…
This work is concerned with asymptotic approximations of the semi-classical Schr\"odinger equation in periodic media using Gaussian beams. For the underlying equation, subject to a highly oscillatory initial data, a hybrid of the Gaussian…
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a…
Universality class of wave chaos emerges in many areas of science, such as molecular dynamics, optics, and network theory. In this work, we generalize the wave chaos theory to cavity lattice systems by discovering the intrinsic coupling of…
We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band's Bloch wave functions. We first explain that the flat bands can be classified into…
We describe mathematically the apparently paradoxical phenomenon that an electronic current in a semiconductor can flow because of collisions, and not despite them. A transport model of charge transport in a one-dimensional semiconductor…
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two…
We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes…