Related papers: Possible Size Dependence of Distribution Functions…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are…
Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
Macroscopic mechanical properties of polymers are determined by their microscopic molecular chain distribution. Due to randomness of these molecular chains, probability theory has been used to find their micro-states and energy…
The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition…
The partition function for a system of non-interacting $N-$particles can be found by summing over all the states of the system. The classical partition function for an ideal gas differs from Bosonic or Fermionic partition function in the…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
Quantum mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle…
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…
Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and…
Long-range forces between macroscopic objects are mediated by light particles that interact with the electrons or nucleons, and include spin-dependent static components as well as spin- and velocity-dependent components. We parametrize the…
Probability density functions (PDF) of statistical distributions of cluster sizes N, where N is the number of particles in the cluster, often seem to have less freedom than expected from considering the number of degrees of freedom at the…
Several materials, such as rocks, powders and molecules, are multi-component systems. However, compared to single-component systems, it is difficult to understand the physical component. In this study, as a coarse-grained model for powders…
We use our recently developed functional bosonization approach to bosonize interacting fermions in arbitrary dimension $d$ beyond the Gaussian approximation. Even in $d=1$ the finite curvature of the energy dispersion at the Fermi surface…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
We investigate how the range of parameters that specify the two-particle distribution function is restricted if we require that this function be obtained from the $n^{\rm th}$ order distribution functions that are symmetric with respect to…
The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
We consider a model of a nanocomposite based on non-interacting spherical single-domain ferroelectric nanoparticles of various sizes embedded in a dielectric matrix. The size distribution function of these nanoparticles is selected as a…