Related papers: Chiral Maxwell waves in continuous media from Berr…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
Weyl degeneracies in spectra of magnetoplasma waves enable nonreciprocal energy flow and topologically protected modes, yet conventional materials require impractical magnetic fields to operate. Developing an effective Hamiltonian framework…
Topological media are gapped or gapless fermionic systems, whose properties are protected by topology, and thus are robust to deformations of parameters of the system and generic. We discuss the class of gapless topological media, which…
The chiral bag model offers a dual description of hadron physics in terms of quarks and hadrons in the sense of Cheshire Cat principle. In this work, we find that, within the chiral bag, confinement is likely caused by monopole…
We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.
Using a nonlinear electrodynamics coupled to teleparallel theory of gravity, three regular charged spherically symmetric solutions are obtained. The nonlinear theory reduces to the Maxwell one in the weak limit and the solutions correspond…
Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a…
The behavior of strongly interacting electrons in bands with Berry curvature is a problem of wide interest. In this paper, we study this problem by numerically studying a fluxed Hubbard-type model on square lattice. Using this model, we…
Topological phases of matter have recently attracted a rather notable attention in the community dealing with the holographic methods applied to strongly interacting condensed matter systems. In particular, holographic models for gapless…
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure…
Electromagnetic topological edge states typically are created in photonic systems with crystalline symmetry and these states emerge because of the topological feature of bulk Bloch bands in momentum space according to the bulk-edge…
In this paper the semi-discrete finite element approximation of initial boundary value problems for Maxwell's equations in nonliear media of Kerr-type is investigated. For the case of N\'ed\'elec elements from the first family, a priori…
Although topological invariants have been introduced to classify the appearance of protected electronic states at surfaces of insulators, there are no corresponding indexes for Weyl semimetals whose nodal points may appear randomly in the…
We study the quasiparticles in chiral double layers with electron pairing within the framework of the Bogoliubov de Gennes equation. In the presence of an edge it is demonstrated that the quasiparticle modes can be distinguished as edge…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
We show that in conventional one-dimensional insulators excess charges created close to the boundaries of the system can be expressed in terms of the Berry phases associated with the electronic Bloch wave functions. Using this…
The scattering of electrically charged fermions on magnetic monopole leads to the Callan-Rubakov problem. We discuss some aspects of this problem for Abelian gauge theories with chiral fermions in a Dirac monopole background. In some cases,…
New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and non-trivial charges are proved. We use the FBI transform to carry out the analysis in phase space. For this purpose, the Maxwell equations…
It is shown that Maxwell's equations in media without source can be written as a contact Hamiltonian vector field restricted to a Legendre submanifold, where this submanifold is in a fiber space of a bundle and is generated by either…
We study Borel systems and continuous systems of measures, with a focus on mapping properties: compositions, liftings, fibred products and disintegration. Parts of the theory we develop can be derived from known work in the literature, and…