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For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions.…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The excess free energy functional of classical density functional theory depends upon the type of fluid model, specifically on the choice of (pair) potential, is unknown in general, and is approximated reliably only in special cases. We…
We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A radiative fluctuation-dissipation…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of…
The paper is devoted to frame expansions in Fr\'echet spaces. First we review some results which concern series expansions in general Fr\'echet spaces via Fr\'echet and General Fr\'echet frames. Then we present some new results on series…
The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical…
We use functional, Fr\'echet, derivatives to quantify how thermodynamic outputs of a molecular dynamics (MD) simulation depend on the potential used to compute atomic interactions. Our approach quantifies the sensitivity of the quantities…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
We consider a simple model of the dynamics of a single electron in a crystal lattice. Although this is a standard problem in condensed matter physics, alternative ways of evaluating a partition function for such a system lead to equalities,…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t…