Related papers: Electromagnetic space-time crystals. II. Fractal c…
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
In this paper the interaction of a scalar field and the electromagnetic field in phase space is analyzed. The scattering process is calculated up to first order in the Planck constant which is obtained by an expansion of the Moyal product…
The relation between the notion of crystalline symmetry and characteristic time intervals when this symmetry could be observed is analyzed. Several time scales are shown to exist for a system of interacting particles. It is only when the…
Relying on Feynman-Kac path-integral methodology, we present a new statistical perspective on wave single-scattering by complex three-dimensional objects. The approach is implemented on three models -- Schiff approximation, Born…
A novel approach to electronic correlations in magnetic crystals which takes into account a dynamical many-body effects is present. In order to to find a frequency dependence of the electron self energy, an effective quantum-impurity…
This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…
A novel approach to electronic correlations and magnetism of crystals based on realistic electronic structure calculations is reviewed. In its simplest form it is a combination of the ``local density approximation'' (LDA) and the dynamical…
Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
We use tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the…
A finite element approach to solve numerically the Takagi-Taupin equations expressed in a weak form is presented and applied to simulate X-ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
In an earlier letter [Ducharme \textit{et al.} Phys. Rev. Lett. \textbf{126}, 134803 (2021)], a solution to the Dirac equation for a relativistic Gaussian electron beam showed that for a diverging beam the spin of each electron is the sum…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…