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The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
The phenomenological evidence of quantum statistical effects in parton physics is here briefly summarized, and the recent good results obtained by parameterizing the parton distributions in terms of Fermi-Dirac and Bose-Einstein statistical…
We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For…
We propose the implementation of a switch of particle statistics with an embedding quantum simulator. By encoding both Bose-Einstein and Fermi-Dirac statistics into an enlarged Hilbert space, the statistics of quantum particles may be…
Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi, and anyonic statistics are proposed. They follow from the R-matrix approach to deformed associative algebras. It is proved that generalized quons have the same main…
Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can…
We will use analytic function theory and Fourier analysis to establish a characterization for some classical umbral calculus, which will focus on the generalization of the evaluation function. Although we cannot cover all the umbral…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
We develop a microscopic formalism to study the fractional quantum Hall plateaus at filling factors $\nu $ away from $1/2\beta$ $\beta$ an integer. The theory is in terms of quasiparticles which carry a charge $e^{\ast}$ equal to…
A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can…
Numerical modelling of quantum effects caused by bosonic or fermionic character of secondaries produced in high energy collisions of different sorts is at the moment still far from being established. In what follows we propose novel…
One remarkable feature of strongly correlated systems is the phenomenon of fractionalization where quasiparticles carry only a fraction of the charge or spin of the elementary constituents. Such quasiparticles often present anyonic…