Related papers: Chains with Fractal Dispersion Law
We determine the probability distribution of the breaking strength for chains of N links, which have been produced by repeatedly breaking a very long chain.
A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
Persistent currents of disordered multichannel mesoscopic rings of spinless interacting fermions threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock methods. The validity of the…
We consider the energy level statistics of non-interacting electrons which diffuse in a $ d $-dimensional disordered metallic conductor of characteristic Thouless energy $ E_c. $ We assume that the level distribution can be written as the…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the…
This paper considers three kinds of length sequences of the complete genome. Detrended fluctuation analysis, spectral analysis, and the mean distance spanned within time $L$ are used to discuss the correlation property of these sequences.…
Based on first-principles calculations we revealed fundamental properties of infinite and finite size monatomic chains of carbon atoms in equilibrium and under an applied strain. Distributions of bond lengths and magnetic moments at atomic…
We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
Fractal structure of shortest paths depends strongly on interresidue interaction cutoff distance. The dimensionality of shortest paths is calculated as a function of interaction cutoff distance. Shortest paths are self similar with a…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we…
The dynamics of two interacting quantum particles on a weakly disordered chain is investigated. Spatial quantum interference between them is characterized through the statistics of two-particle transition amplitudes, related to Hanbury…
Generalized dispersion relations are discussed for unphysical particles, e.g. confined degrees of freedom that are not present in the physical spectra but can give rise to observable bound states. While in general the propagator of the…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows…
The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^\gamma$. It is shown that $\gamma$ is quantitatively related to…