Related papers: Response to the comment on "Do Bloch waves interfe…
We point out that argumentation presented in [Phys. Lett. A 417, 127699 (2021)], leading to the conclusion that in periodic systems there is a superselection principle forbidding two different Bloch states to form a coherent superposition…
Here we show that two Bloch states, which are energy eigenstates of a quantum periodic potential problem, with different wavevectors can not be linearly superposed to display quantum interference of any kind that captures the relative phase…
In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary…
Suppose that particle detectors are placed along a Cauchy surface $\Sigma$ in Minkowski space-time, and consider a quantum theory with fixed or variable number of particles (i.e., using Fock space or a subspace thereof). It is…
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
We show that the mechanism of gap formation has a resonance nature. The special real fundamental solutions were discovered which `paradoxically' have knot distribution with a period coinciding with that of potential at all energies of the…
We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore we discuss the relations of…
We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion…
We suggest a novel concept in the soliton switching based on the Bloch-wave filtering in periodic photonic structures. Taking a binary waveguide array as an example, we demonstrate that spatial solitons that belong to different spectral…
We study the scattering of scalar waves propagating on the global monopole background. Since the scalar wave operator in this topological defect is not essentially self-adjoint, its solutions are not uniquely determined until a boundary…
Under the action of a weak constant force a wavepacket in periodic potential undergoes periodic oscillations in space, returning to the initial position after one oscillation cycle. This wave phenomenon, known as Bloch oscillations (BOs),…
This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in…
This paper is a continuation of a previous work by two of the Authors on long time existence for Boussinesq systems modeling the propagation of long, weakly nonlinear water waves. We provide proofs on examples not considered previously in…
We study the Bloch theorem which states absence of the spontaneous current in interacting electron systems. This theorem is shown to be still applicable to the system with the magnetic field induced by the electric current. Application to…
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…
We study the local and global well-posedness of the periodic boundary value problem for the nonlinear Schr\"odinger-Boussinesq system. The existence of periodic pulses as well as the stability of such solutions are also considered.
Our interest itself of this paper is strongly inspired from an open problem in the paper [1] published by D'Abbicco. In this article, we would like to study the Cauchy problem for a weakly coupled system of semi-linear structurally damped…
A family of generalized Korteweg-de Vries-Burgers equations in one space dimension with a nonlinear source is considered. The purpose of this contribution is twofold. On one hand, the local well-posedness of the Cauchy problem on periodic…
For systems which contain both superselection structure and constraints, we study compatibility between constraining and superselection. Specifically, we start with a generalisation of Doplicher-Roberts superselection theory to the case of…
We prove that the subquartic wave equation on the three dimensional ball $\Theta$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_{s<1/2} H^s(\Theta)$. We…