Related papers: Conservation of Statistics and Generalized Grassma…
A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example,…
The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic…
Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…
Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins of such exchange force ideas, the validity for…
We continue the program started in cond-mat/9809384 and explain the statistics of the excitations for the generalizations of the paired states in the quantum Hall effect in terms of the parafermion statistics. We show that these excitations…
A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations…
In this work, the proofs concerning the continuity of the disequilibrium, Shannon information and statistical complexity in the space of distributions are presented. Also, some results on the existence of Shannon information for continuous…
Quantum systems invariant under particle exchange are either Bosons or Fermions, even though quantum theory in principle admits more general behavior under permutations. But why do we not observe such "paraparticles" in nature? The analysis…
I recently proposed a method of bosonization valid for systems of an even number of fermions whose partition function is dominated at low energy by bosonic composites. This method respects all symmetries, in particular fermion number…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
The seven binary quantum numbers that distinguish fundamental fermions have been shown to be conserved in decays and interactions. Here applications of this law are clarified to take account of odd (uct) and even (dsb) parity quarks…
We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection…
Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional…
We consider a version of generalised $q$-oscillators and some of their applications. The generalisation includes also "quons" of infinite statistics and deformed oscillators of parastatistics. The statistical distributions for different…
Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a…
After some general comments about statistics and the TCP theorem, I discuss experimental searches for violations of the exclusion principle and theories which allow for such violations.
We investigate the dynamics of pairs of Fermions and Bosons released from a box and find that their populations have unique generic properties ensuing from the axioms of quantum statistics and symmetries. These depend neither on the…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
We describe fermions in terms of a classical statistical ensemble. The states $\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability…
In contrast to classical physics, quantum mechanics divides particles into two classes-bosons and fermions-whose exchange statistics dictate the dynamics of systems at a fundamental level. In two dimensions quasi-particles known as 'anyons'…