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We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years,…
We present a scaling analysis of electronic and transport properties of metal-semiconducting carbon nanotube interfaces as a function of the nanotube length within the coherent transport regime, which takes fully into account atomic-scale…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
The Aubry-Andre model is a one-dimensional lattice model for quasicrystals with localized and delocalized phases. At the localization transition point, the system displays fractal spectrum, which relates to the Hofstadter butterfly. In this…
Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic…
Traditional band theory of perfect crystalline solids often uses as input the structure deduced from diffraction experiments; when modeled by the minimal unit cell this often produces a spatially averaged model. The present study…
We study numerically and analytically the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations…
The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to…
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to…
In this communication, we study the level-spectra statistics when a noninteracting electron gas is confined in \textit{Sierpi\'{n}ski Carpet} (\textit{SC}) lattices. These \textit{SC} lattices are constructed under two representative…
We study the stationary state of a Poisson problem for a system of N perfectly conducting metal balls driven by electric forces to move within a medium of very low electrical conductivity onto which charges are sprayed from outside. When…
The theory of resource distribution in self-organizing systems on the basis of the fractal-cluster method has been presented. In turn, the fractal-cluster method is based on the fractal-cluster relations of V.P. Burdakov and the analytical…
We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are line-like excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form…
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional…