相关论文: Electronic fractal patterns in building Sierpinski…

Electron energy loss spectroscopy is consolidating as a powerful tool to explore electronic (as well as vibrational) excitations of matter, including molecules. Performed in a scanning transmission electron microscope, this technique is…

Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…

The spectral properties of itinerant 2D systems with (nearly) ferromagnetic ground state are studied within the spin-fermion and the classical s-d exchange models. While the former model describes the effect of collective magnetic…

Supermoir\'e structures (SMS), formed by overlapping moir\'e-patterns in van der Waals heterostructures, display complex behaviour that lacks a comprehensive low-energy theoretical description. We demonstrate that these structures can form…

We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries -- termed "Pascal's triangle symmetries" -- which provides a natural $U(1)$ generalization of a spin-(1/2) system with Sierpinski triangle…

Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Many fractals are constructed as natural limits of certain sets with a simpler structure:…

Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and…

Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, three-dimensional dynamic modes that occur at microwave frequencies. During dynamic…

Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…

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…

The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…

A method is introduced to isolate and measure the electrical transport properties of individual single-walled carbon nanotubes (SWNTs) aligned on an ST-cut quartz, from room temperature down to 2 K. The diameter and chirality of the…

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…

We construct transported PDEs on self-similar fractal domains from reference equations posed on the unit interval, and derive explicit self-similar interacting particle systems that approximate the resulting dynamics. The construction…

We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…

Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \textit{Sierpi\'{n}ski} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed…

Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…

The first-principles calculations have been performed to investigate the ground state properties of cubic scandium trifluoride (ScF$_3$) perovskite. Using modified hybrid exchange-correlation functionals within the density functional theory…

We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy (known as entanglement entropy) and the entanglement contour in the scaling limit. Adopting quadratic fermionic models on…

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…