相关论文: Magnetostatic problems in fractal domains

Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem.…

The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and…

Inspired on the continued-fraction technique to solve the classical Fokker--Planck equation, we develop continued-fraction methods to solve quantum master equations in phase space (Wigner representation of the density matrix). The approach…

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a $Q$ -state Potts cluster, is solved in two dimensions. The dimension $\hat f(\theta)$ of the…

Magnetism is a rich subject touching all aspects of physics. My goal with this dissertation is to explore spin and magnetic moments in \emph{relativistic} mechanics from both a quantum and classical perspective. We emphasize the special…

The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…

We study time-harmonic scattering in $\mathbb{R}^n$ ($n=2,3$) by a planar screen (a "crack" in the context of linear elasticity), assumed to be a non-empty bounded relatively open subset $\Gamma$ of the hyperplane $\mathbb{R}^{n-1}\times…

We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…

Fracton topological order hosts fractionalized point-like excitations (e.g., fractons) that have restricted mobility. In this article, we explore even more bizarre realization of fracton phases that admit spatially extended excitations with…

Manipulating magnetic domains is essential for many technological applications. Recent breakthroughs in Antiferromagnetic Spintronics brought up novel concepts for electronic device development. Imaging antiferromagnetic domains is of key…

The convergence of iterative schemes to achieve self-consistency in mean field problems such as the Schr\"odinger-Poisson equation is notoriously capricious. It is particularly difficult in regimes where the non-linearities are strong such…

We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a…

Scattering of nonstationary electromagnetic fields from axially symmetrical bodies is numerically investigated. Simulations are performed using the time- and frequency-domain approaches. Computational results obtained for a finite perfectly…

We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary…

This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…

Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring…

We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different…

Based on the PXP model adapted for Rydberg-blockaded chains, we investigate dynamics of topological domain walls between different quantum many-body scar states of $\mathbb{Z}_2$ symmetry. It is found that, the domain walls not only possess…