Related papers: Generalized Cluster States Based on Finite Groups
This if the final paper in the seriesContinuous Quivers of Type $A$. In this part, we generalize existing geometric models of type $A$ cluster structures to the new $\mathbf E$-clusters introduced in part (III). We also introduce an…
We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
Associated with some finite dimensional algebras of global dimension at most 2, a generalized cluster category was introduced in \cite{Ami3}, which was shown to be triangulated and 2-Calabi-Yau when it is $\Hom$-finite. By definition, the…
We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein-Retakh, and are inspired by the emerging theory of…
The construction of partially compactified cluster algebras on coordinate rings is handled by using codimension 2 arguments on cluster covers. An analog of this in the quantum situation is highly desirable but has not been found yet. In…
This is a continuation of the preceding paper (hep-ph/0108219). First of all we make a brief review of generalized coherent states based on Lie algebra su(1,1) and prove that the resolution of unity can be obtained by the curvature form of…
Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group…
In this tutorial I intend to present some of the results I obtained through my PhD work in the "quantum optics group of the University of Isfahan" under consideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and advisor,…
In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
We introduce new objects, called $(G,c)$-bands, associated with a simple simply-connected algebraic group $G$, and a Coxeter element $c$ in its Weyl group. We show that bands of a given type are the $K$-points of an infinite dimensional…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
We provide a quantitative analysis of the splittings in low-lying numerical entanglement spectra (ES), at given momentum, of a number of quantum states that can be identified, based on "Li-Haldane state-counting", as ground states of…
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum…
We present the cluster-type entangled coherent states (CTECS) and discuss their properties. A cavity QED generation scheme using suitable choices of atom-cavity interactions, obtained via detunings adjustments and the application of…
The cluster multiplication formulas for a generalized quantum cluster algebra of Kronecker type are explicitly given. Furthermore, a positive bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-basis of this algebra is constructed.
We generalize the concept of local states (LS) for the prediction of high-dimensional, potentially mixed chaotic systems. The construction of generalized local states (GLS) relies on defining distances between time series on the basis of…
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…
The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently they were generalized to quantum affinizations of quantum Kac-Moody algebras associated with a wide…