Related papers: Conservation of Statistics and Generalized Grassma…
The quon algebra gives a description of particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons, for which $q = +1$, and fermions, for which $q = -1$.…
We calculate the baryon factorial cumulants assuming arbitrary short-range correlations and the global baryon number conservation. The general factorial cumulant generating function is derived. Various relations between factorial cumulants…
We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric algebra and show that it can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are…
We study the trace of the exponentials of general fermion bi-linears, including pairing terms, and including non Hermitian forms. In particular, we give elementary derivations for determinant and pfaffian formulae for such traces, and use…
We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent…
Non-Abelian anyons have garnered extensive attention for obeying exotic non-Abelian statistics and having potential applications to fault-tolerant quantum computing. While the prior research has predominantly focused on non-Abelian…
In a recent paper, Goyt and Sagan studied distributions of certain set partition statistics over pattern restricted sets of set partitions that were counted by the Fibonacci numbers. Their study produced a class of $q$-Fibonacci numbers,…
We analyse the homogeneous parts of Clifford and meson algebras and point out that for the Clifford algebra it is related to fermionic statistics, that is, to fermionic parastatistics of order 1 while for the meson algebra it is related to…
Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles…
We calculate the 1/N corrections to the probability distributions of quadratic discrepancies for sets of N random points. This is achieved by the introduction of fermionic variables. We give the diagrammatic expansion up to and including…
A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q…
A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of canonically conjugate variables. These corrections can be…
We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for…
Since baryon number B and lepton number L are no longer automatically conserved once the standard model is extended to include supersymmetry, the usually assumed conservation of R parity is an imposed condition. For a more satisfactory…
In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does…
The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We…
There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance ("fermion number"). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
If the generalized statistics suggested by Tsallis are used in statistical mechanics, the fluctuation-dissipation theorem no longer holds. Only in the limiting case where Boltzmann statistics are recovered is the theorem applicable. In…
A long-standing problem with the many-body approximations for interacting condensed bosons has been the dichotomy between the ``conserving'' and ``gapless'' approximations, which either obey the conservations laws or satisfy the…