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Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian $q$-Oscillator and their Entanglement
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this parer, $q$-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 para-Grassmannian 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 pseudo-Hermitian coherent state introduced, and the method also developed to define pseudo-Hermitian 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 multi-level 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.
Keywords: para-Grassmann variables; coherent state; squeezed state; pseudo-Hermiticity; entanglement. 
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     title = {Para-Grassmannian {Coherent} and {Squeezed} {States} for {Pseudo-Hermitian} $q${-Oscillator} and their {Entanglement}},
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}
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Yusef Maleki. Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian $q$-Oscillator and their Entanglement. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a83/

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