相关论文: Detailed Balance and Intermediate Statistics
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
An anyon exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane[1]. The relevant past studies had considered only anyon systems without any physical boundary but…
We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R^2 with anyon statistics. Sufficient conditions are given which guarantee the existence of wave operators and the unitarity of the…
In social contexts where individuals consume varying amounts, such as shared meals or bar gatherings, splitting the total bill equally often yields surprisingly fair outcomes. In this work, we develop a statistical physics framework to…
The phenomenological motivations, the expressions and the comparison with experiment of the parton distributions inspired by the quantum statistics are described. The Fermi-Dirac expressions for the quarks and their antiparticles…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…
We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane's…
We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
Equilibrium distribution of interacting ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For an arbitrarily given realization of the disorder, an exact solution of the equation is…
We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…
The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is…
The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same…
In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
We consider the recent description of elementary particles in terms of Quantum Mechanical Kerr-Newman Black Holes, a description which provides a rationale for and at the same time reconciles the Bohm-hydrodynamical formulation on the one…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…