Related papers: Pairings and actions for dynamical quantum groups
By using the quantum Yang-Baxterization approach, we investigate the dynamics of quantum entanglement under the actions of different Hamiltonians on the different two-qubit input states and analyze the effects of the Yang-Baxter operations…
Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
We use a tensor C*-category with conjugates and two quasitensor functors into the category of Hilbert spaces to define a *-algebra depending functorially on this data. If one of them is tensorial, we can complete in the maximal C*-norm. A…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
We study ${\rm GL}_N$ rational $R$-matrix, which turns into the 11-vertex $R$-matrix in the $N=2$ case. First, we describe its relations to dynamical and semi-dynamical $R$-matrices using the IRF-Vertex type transformations. As a by-product…
We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is…
The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation introduced by Gervais, Neveu, and Felder. The QDYB equation and its quasiclassical analogue (the classical dynamical…
The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent…
Since the 1970s, spin-selective reactions of radical pairs have been modelled theoretically by adding phenomenological rate equations to the quantum mechanical equation of motion of the radical pair spin density matrix. Here, using a…
In this paper we consider dynamical r-matrices over a nonabelian base. There are two main results. First, corresponding to a fat reductive decomposition of a Lie algebra $\frakg =\frakh \oplus \frakm$, we construct geometrically a…
In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation…
Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and…
An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
A completely integrable dynamical system in discrete time is studied by means of algebraic geometry. The system is associated with factorization of a linear operator acting in a direct sum of three linear spaces into a product of three…
Spectral functions are central to link experimental probes to theoretical models in condensed matter physics. However, performing exact numerical calculations for interacting quantum matter has remained a key challenge especially beyond one…