Related papers: Calculating statistical distributions from operato…
In this paper we investigate a quantum stochastic calculus build of creation, annihilation and number of particles operators which fulfill some deformed commutation relations. Namely, we introduce a deformation of a number of particles…
A procedure to derive the partition function of non-interacting particles with exotic or intermediate statistics is presented. The partition function is directly related to the associated creation and annihilation operators that obey some…
We give the normal and anti-normal order expressions of the number operator to the power $k$ by using the commutation relation between the annihilation and creation operators. We use those expressions to give general formulae for functions…
Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between…
The simple algebras of a dressed operator, which is composed of a dressing and a residual operators, are averaged following a proper statistics of the dressing one. In the Bose-Einstein statistics, a (fermionic) Calogero-Vasiliev…
We show how to calculate the operator algebra and the operator Lie algebra of a stochastic labelled-graph grammar. More specifically, we carry out a generic calculation of the product (and therefore the commutator) of time-evolution…
This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by $n$ particles. First, we…
In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
We present a formulation of the deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between the Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
An entropic approach to formulating uncertainty relations for the number-annihilation pair is considered. We construct some normal operator that traces the annihilation operator as well as commuting quadratures with a complete system of…
In order to enlarge the present arsenal of semiclassical toools we explicitly obtain here the Husimi distributions and Wehrl entropy within the context of deformed algebras built up on the basis of a new family of q-deformed coherent…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
This paper generalises inference functions (Godambe, 1960) to distributional statistical models, in which each probability measure is represented by a distribution--kernel pair $(T_\theta, \varphi) \in \mathcal S'(\mathbb R) \times \mathcal…
We discuss the probability distribution for the "size" of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards larger operators. Initially, the rate is exponential…
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…
We adopt an operatorial method based on the so-called creation, annihilation and number operators in the description of different systems in which two populations interact and move in a two-dimensional region. In particular, we discuss…