Related papers: Particles, Generalized Statistics and Categories
Cosmological solutions of Einstein's equations for equilibrium statistical systems of particles with scalar interaction are investigated. It is shown that the scalar field can effectively change the state equation of a statistical system,…
We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…
The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible,…
This paper is devoted to linear space representations of contextual probabilities - in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the…
Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as…
Quantum states of systems made of many identical particles, e.g. those described by Fermi-Hubbard and Bose-Hubbard models, are conveniently depicted in the Fock space. However, in order to evaluate some specific observables or to study the…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics.
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
A family of probability distributions attached to a class of generalized weighted Bergman spaces on the Poincar\'e disk are introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
We investigate the expression of natural numbers in any base from a quantum point of view. In particular, resorting to the one-to-one correspondence between natural numbers and Fock states, we construct a set of multiboson operators and a…
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…
In this paper we propose a unified statistics of Bose-Einstein and Fermi-Dirac statistics by suggesting that every particle can be associated with matter or fundamental forces with certain probability. The main Justification for this…
An exposition of the different definitions and approaches to quantum statistics is given, with emphasis in one-dimensional situations. Permutation statistics, scattering statistics and exclusion statistics are analyzed. The Calogero model,…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…