Related papers: Spectrum generating algebra and coherent states of…
In the paper we describe the C*-algebras of noncommutative spherical tight frames over some C*-algebras and then apply to study the noncommutative version of the universal classifying space.
We extend the study on the algebraic structure of the $su(n)$ color Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two $gl(n|m)$ loop…
We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These…
In this paper we consider shift operators, self-adjoint, unitary and normal operators on the standard module over a unital C*-algebra A. We define various generalized spectra in A of these operators, give description of such spectra of…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We present protocols for the generation of high-dimensional entangled states of anharmonic oscillators by means of coherent manipulation of light-matter systems in the ultrastrong coupling regime. Our protocols consider a pair of…
We study the universal C^*-algebras generated by n projections $p_1, >..., p_n$ subject to the relation $p_1+... p_n = \lambda 1$, $\lambda \in \mathbb R$. The questions of when these C^*-algebras are type I, nuclear or exact are…
A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter…
We study a supersymmetric 2-dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2$\vert$1), formulate it on the superspace, and discuss its physical spectrum.
Cluster states are versatile quantum resources and an essential building block for measurement-based quantum computing. The possibility to generate cluster states in specific systems may thus serve as an indicator regarding if and to what…
We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…
We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete phase spaces based on finite fields. To do…
Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…
Two types of the coherent states for two parameter deformed multimode oscillator system are investigated. Moreover, two parameter deformed $gl(n)$ algebra and deformed symmetric states are constructed.
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
We review classical properties of harmonic-oscillator coherent states. Then we discuss which of these classical properties are preserved under the group-theoretic generalization of coherent states. We prove that the generalized coherent…
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…
Full coherent control and generation of superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology and continuous-variable…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a…