Related papers: New theory of periodical systems by finite interva…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown…
Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…
The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We present a new method of gap control in two-dimensional periodic systems with the perturbation consisting of a second-order differential operator and a family of narrow potential `walls' separating the period cells in on direction. We…
Recently, we have discovered a new concept of permanent wave resonance with potential spatial oscillations. This means the constant wave swinging frequency on the whole energy intervals of spectral forbidden zones destroying physical…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
The physical mechanism of phenomenon is explained as a result of inequality of forward and reversed processes in optics. The importance of experimental study of its invariance relation is discussed.
We theoretically study the spin-wave spectra in magnonic waveguides periodically patterned with square anti-dots in nanoscale with pinned magnetization at the edges. We show that the breaking of the mirror symmetry of the waveguide by the…
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in…
We consider the first order periodic systems perturbed by a $2N\ts 2N$ matrix-valued periodic potential on the real line. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the…
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
We present a micromagnetic analysis of spin-wave propagation in a magnonic crystal realized as a permalloy spin-wave waveguide with a spatial periodical variation of its saturation magnetization. Frequency band gaps were clearly observed in…
We identify explicit conditions on geometry and material contrast for creating band gaps in 2-d photonic and 3-d acoustic crystals. This approach is novel and makes use of the electro-static and quasi-periodic source free resonances of the…
We give a mathematical analysis of the periodic band inversion phenomenon observed by Tan--Devakul for an electron in a two-dimensional periodic potential coupled to a circularly polarized photon cavity mode. In the strong-coupling limit,…
Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic…
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,…