Related papers: Topological Theory for Perfect Metasurface Isolato…
Two new formulations of Bell's theorem are given here. First, we consider a definite set of two entangled photons with only two polarization directions, for which Bell's locality assumption is violated for the case of perfect correlation.…
We consider linear and nonlinear coherent perfect absorbers (CPAs) in multidimensional geometries and construct explicitly the respective perfectly absorbed solutions. The multidimensional CPAs have a structure of the so-called simple…
We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…
We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial"…
Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order…
We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many…
In this work, we study the transmission properties of one dimensional finite periodic systems with $\mathcal{PT}$-symmetry. A simple closed form expression is obtained for the total transmittance from a lattice of N cells, that allows us to…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
Modern nanophotonic and meta-optical devices utilize a tremendous number of structural degrees of freedom to enhance light--matter interactions. A fundamental question is how large such enhancements can be. We develop an analytical…
The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent, covering more than one lattice site. We expand the well studied Totally Asymmetric Exclusion…
We prove a general relative higher index theorem for complete manifolds with positive scalar curvature towards infinity. We apply this theorem to study Riemannian metrics of positive scalar curvature on manifolds. For every two metrics of…
This paper provides an Open Mapping Theorem for topological modules over rings that have a zero sequence consisting of units. As an application it is shown that there is a unique complete and metrisable topology on finitely generated…
It is theoretically known that a pair of phase conjugating surfaces can function as a perfect lens, focusing propagating waves and enhancing evanescent waves. However, the known experimental approaches based on thin sheets of nonlinear…
Energy of propagating electromagnetic waves can be fully absorbed in a thin lossy layer, but only in a narrow frequency band, as follows from the causality principle. On the other hand, it appears that there are no fundamental limitations…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
There are several ideal boundaries and completions in General Relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator $L$. As emphasized in a…
Leveraging topological properties in the response of electromagnetic systems can greatly enhance their potential. Although the investigation of singularity-based electromagnetics and non-Hermitian electronics has considerably increased in…
The research in topological materials and meta-materials reached maturity and is now gradually entering the phase of practical applications and devices. However, scaling down the experimental demonstrations definitely presents a challenge.…
In this work we propose and theoretically characterize optical isolators consisting of an all-dielectric and non-magnetic resonator featuring an intensity-dependent refractive index and a strong coherent field propagating in a single…
F. Escalante and T. Gallai studied in the seventies the structure of different kind of separations and cuts between a vertex pair in a (possibly infinite) graph. One of their results is that if there is a finite separation, then the optimal…