On Linear Differential Equations Involving a Para-Grassmann Variable

Mansour, Toufik; Schork, Matthias

doi:10.3842/sigma.2009.073

Cited by 5 publications

(2 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The study of Grassmann variables and their different generalizations have attracted a great deal of attention in the last few decades [1][2][3][4][5][6][7][8]. This is due to the fact that these variables are useful mathematical tools for studying various problems in theoretical physics and quantum optics [7,[9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Multi-mode entangled states represented as Grassmannian polynomials

Maleki

2016

Quantum Inf Process

View full text Add to dashboard Cite

We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map the Hilbert space of the finite-dimensional multi-mode states to the space of some Grassmannian polynomial functions. These Grassmannian polynomials form a well-defined space in the framework of Grassmann variables; namely Grassmannian representative space. Therefore, a quantum state can be uniquely defined and determined by an element of Grassmannian representative space. Furthermore, the Grassmannian representatives of some maximally entangled states are considered, and it is shown that there is a tight connection between the entanglement of the states and their Grassmannian representatives.

show abstract

Section: Introductionmentioning

confidence: 99%

Multi-mode entangled states represented as Grassmannian polynomials

Maleki

2016

Quantum Inf Process

View full text Add to dashboard Cite

show abstract

“…In the same direction, the big number of works on coherent states and their various applications, indicates an excited interest of today's researchers in this field [7,8,9,10,11,12,13,14,15,16,17,18,19]. Among all, Grassmannian coherent states and their generalizations have been widely investigated in recent years, and various applications of Grassmann variables have been studied in theoretical physics and quantum optics [16,17,19,20,21]. In [22], the authors focused on the q-oscillator algebra and introduced appropriate coherent states based on para-Grassmann variables.…”

Section: Introductionmentioning

confidence: 99%

Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement

Maleki¹

2011

SIGMA

View full text Add to dashboard Cite

Abstract. In this paper, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied. Also, some basic properties of these states is surveyed. The over-completeness property of the paraGrassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stability of coherent and squeezed states discussed. The pseudo-Hermitian supercoherent states as the product of a pseudo-Hermitian bosonic coherent state and a para-Grassmannian pseudoHermitian coherent state introduced, and the method also developed to define pseudoHermitian supersqueezed states. It is also argued that, for q-oscillator algebra of k + 1 degree of nilpotency based on the changed ladder operators, defined in here, we can obtain deformed SU q 2 (2) and SU q 2k (2) and also SU q 2k (1, 1). Moreover, the entanglement of multilevel para-Grassmannian pseudo-Hermitian coherent state will be considered. This is done by choosing an appropriate weight function, and integrating over tensor product of PGPHCSs.

show abstract

Generalized Grassmann variables for quantum kit (k-level) systems and Barut–Girardello coherent states for su(r + 1) algebras

Daoud

Gouba

2017

Journal of Mathematical Physics

View full text Add to dashboard Cite

This paper concerns the construction of su(r + 1) Barut-Girardello coherent states in term of generalized Grassmann variables. We first introduce a generalized Weyl-Heisenberg algebra A(r) (r ≥ 1) generated by r pairs of creation and annihilation operators. This algebra provides a useful framework to describe qubit and qukit (k-level) systems. It includes the usual Weyl-Heisenberg and su(2) algebras. We investigate the corresponding Fock representation space. The generalized Grassmann variables are introduced as variables spanning the Fock-Bargmann space associated with the algebra A(r). The Barut-Girardello coherent states for su(r + 1) algebras are explicitly derived and their over-completion properties are discussed.

show abstract

On Linear Differential Equations Involving a Para-Grassmann Variable

Cited by 5 publications

References 49 publications

Multi-mode entangled states represented as Grassmannian polynomials

Multi-mode entangled states represented as Grassmannian polynomials

Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement

Generalized Grassmann variables for quantum kit (k-level) systems and Barut–Girardello coherent states for su(r + 1) algebras

Contact Info

Product

Resources

About