Related papers: Linearized spectral decimation in fractals

In view of promising applications of fractal nanostructures, we analyze the spectra of quantum particles in the Sierpinski carpet and study the non-correlated electron gas in this geometry. We show that the spectrum exhibits scale…

Tower of States analysis is a powerful tool for investigating phase transitions in condensed matter systems. Spontaneous symmetry breaking implies a specific structure of the energy eigenvalues and their corresponding quantum numbers on…

Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of…

The cosmic ray energy distributions contain spectral features, that is narrow energy regions where the slope of the spectrum changes rapidly. The identification and study of these features is of great importance to understand the…

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is…

When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…

We study the behaviour of the power spectrum (PS) in the case of fractal structures. We show that in this case the main observational features of the PS, the large scale flattening and the scaling of the amplitude with sample depth, are…

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…

Using a recently introduced mapping between a scalar elastic network tethered at its boundaries and a diffusion problem with permanent traps, we study various vibrational properties of progressively tethered disordered fractals. Different…

We explore the sensitivity of several core-level spectroscopic methods to the underlying atomistic structure by using the water molecule as our test system. We first define a metric that measures the magnitude of spectral change as a…

Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…

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…

We investigate the possibility, in nuclear fragmentation, to extract information on nuclear density at break-up from fragment kinetic energy spectra using a simultaneous scenario for fragment emission. The conclusions we derive are…

The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…

We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using…

We explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique…

The spectral statistics of nuclei undergo through the major forms of radioactive decays ((\alpha)(\beta^-), and(\beta^+) (or EC)) and also stable nuclei are investigated. With employing the MLE technique in the nearest neighbor spacing…

We study spectra of noncommutative dynamical systems, representations of fractal groups, and regular graphs. We explicitly compute these spectra for five examples of groups acting on rooted trees, and in three cases obtain totally…

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…

Flux-energy and angle-energy diagrams for an exact three-dimensional Hamiltonian of the Bloch electron in a uniform magnetic field are analyzed. The dependence of the structure of the diagrams on the direction of the field, the geometry of…