Related papers: Statistics and Quantum Group Symmetries
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
We propose a new kind of quantum phase transition in phase separated mixtures of Bose-Einstein condensates. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of…
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…
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial…
It is shown that a dynamical quantum group arising from a vertex-IRF transformation has a second realization with untwisted dynamical multiplication but nontrivial bigrading. Applied to the $\hbox{SL}(2;\mathbb{C})$ dynamical quantum group,…
In multiparticle quantum interference, bosons show rather generally the tendency to bunch together, while fermions can not. This behavior, which is rooted in the different statistics of the particles, results in a higher coincidence rate…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
We investigated the entropy bounds of the three types of statistics: para-Bose, para-Fermi and infinite statistics. We showed that the entropy bounds of the conventional Bose, Fermi statistics and their generalizations to parastatistics…
Quantum field theory allows more general symmetries than groups and Lie algebras. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now. Nowdays many examples of symmetries of…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with…
By analyzing the BCS-BEC crossover, I found that because of the pairing interactions,a continuous family of quantum statistics interpolating between fermions and bosons is possible, although it seems incapable to construct reasonable wave…
Quantum mechanics allows paraparticles with mixed Bose-Fermi statistics that have not been experimentally confirmed. We propose a trapped-ion scheme whose effective dynamics are equivalent to a driven para-Bose oscillator of even order. Our…
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n. We show that these quantum groups can be realized as Drinfel'd doubles of certain Hopf subalgebras with respect…