Related papers: Electron distributions of molecular domains: canon…
The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum…
Although compartmental dynamical systems are used in many different areas of science, model selection based on the maximum entropy principle (MaxEnt) is challenging because of the lack of methods for quantifying the entropy for this type of…
We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
Recent theoretical results renewed the interest in charged particle multiplicity distributions. The Shannon entropy of such distributions is conjectured to be related to the entanglement or von Neumann entropy of partonic quantum system. In…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…
The semi-inclusive properties of the system of neutral and charged particles with net charge equal to zero are considered in the grand canonical, canonical and micro-canonical ensembles as well as in micro-canonical ensemble with scaling…
An electron density functional approach for the calculation of the nuclear multipole moments is presented. The electronic matrix elements entering the experimentally observed hyperfine electron-nucleus interaction constants in atoms are…
Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster…
Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. Remarkably, these are revealed in one and two electron molecular systems if the realm of the nuclear charge is extended to be…
We consider free electrons in rectangular quantum dots, with either hard wall boundary conditions or anharmonic confinement. In both cases, due to finite size effects, a homogeneous electric field applied along one of the rectangular axis…
It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn…
The electronic distribution of a molecular domain is examined in this study. A theoretical formulation of quantum molecular properties is presented using the Quantum Expectation Identity theorem (QEI), with a focus on the three-state model…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
We study an electron distribution under a quasiperiodic potential in light of hyperuniformity, aiming to establish a classification and analysis method for aperiodic but orderly density distributions realized in, e.g., quasicrystals. Using…
The exact universal functional of integer charge leads to an extension to fractional charge asymptotically when it is applied to a system made of asymptotically separated densities. The extended functional is asymptotically local and is…
This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized…
In the past two decades, geometric phases have provided a powerful new way of looking at quantum mechanical systems, manifesting themselves in subtle but observable ways. Here, we use them to define a versatile function ("distribution of…
Statistical mechanics reveals that the properties of a macroscopic physical system emerge as an average over an ensemble of statistically independent microscopic subsystems, each occupying a specific microstate. In the study of quantum…
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…