Related papers: Fractional exclusion statistics in general systems…
We consider N particles interacting pair-wise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically, its classical canonical partition function for the repulsive regime is known in the…
Exact and approximate expressions for thermodynamic characteristics of heated matter, which consists of particles with finite mass-widths, are constructed. They are expressed in terms of Fermi/Bose distributions and spectral functions,…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as…
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
The facilitated simple exclusion process (FEP) is a one-dimensional exclusion process with a dynamical constraint. We establish bounds on the mixing time of the FEP on the segment, with closed boundaries, and the circle. The FEP on these…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad…
The paper analyses the convergence of the $p$-version of the FEM when the solution is piecewise analytic function. It focuses on pointwise convergence of the gradient. It shows that at boundary the rate is different than inside the element…
The statistical mechanics of a cloud of particles interacting via their gravitational potentials is an old problem which encounters some issues when the traditional Boltzmann-Gibbs statistics is applied. In this article, we consider the…
In this paper the classical Euler-Bernoulli beam (CEBB) theory is reformulated utilising fractional calculus. Such generalisation is called fractional Euler-Bernoulli beams (FEBB) and results in non-local spatial description. The parameters…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
A consistent local approach to the study of interacting relativistic fermion systems with a condensation of bare particles in its ground or vacuum state, which may has a finite matter density, is developed. The attention is payed to some of…
The low energy properties of the one-dimensional anyon gas with $\delta$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…
We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes…
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…