Related papers: Complexity of multidimensional hydrogenic systems
The radial expectation values of the probability density of a quantum system in position and momentum spaces allow one to describe numerous physical quantities of the system as well as to find generalized Heisenberg-like uncertainty…
We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global…
Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for $N$-fermion $d$-dimensional systems. The contributions of both spatial and spin degrees of freedom…
A recently developed density functional method, within Hohenberg-Kohn-Sham framework, is used for faithful description of atoms, molecules in Cartesian coordinate grid, by using an LCAO-MO ansatz. Classical Coulomb potential is obtained by…
We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang…
Differential shrinkage in particulate quasi-brittle materials causes microcracking which reduces durability in these materials by increasing their mass transport properties. A hydro-mechanical three-dimensional periodic network approach was…
This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…
The statistical measures of complexity defined by Lopez-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison and Landsberg (SDL) are calculated as functions of the number of particles for four quantum many-body systems, i.e. atoms, nuclei,…
Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…
{We study in some details the statistical properties of the turbulent 2-phase interstellar atomic gas.{We present high resolution bidimensional numerical simulations of the interstellar atomic hydrogen which describe it over 3 to 4 orders…
The structures, as building-blocks for designing functional nanomaterials, have fueled the development of versatile nanoprobes to understand local structures of noncrystalline specimens. Progresses in analyzing structures of individual…
We use a two-fluid model combining the quantum Green's function technique for the electrons and a classical HNC description for the ions to calculate the high-density equation of state of hydrogen. This approach allows us to describe fully…
Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic…
We study two types of intrinsic uncertainties, statistical errors and system size effects, in estimating shear viscosity via equilibrium molecular dynamics simulations and compare them with the corresponding uncertainties in evaluating the…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
We apply the statistical measure of complexity, introduced by L\'{o}pez-Ruiz, Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact via a repulsive hard-core potential. We employ the momentum distribution of this…
The role of inhomegeneity in determining the properties of correlated electron systems is poorly understood because of the dearth of structural probes of disorder at the nanoscale. Advances in both neutron and x-ray scattering…