Generalized Grassmannian coherent states for pseudo-Hermitian<i>n</i>-level systems

Najarbashi, G.; Fasihi, M. A.; Fakhri, H.

doi:10.1088/1751-8113/43/32/325301

Cited by 13 publications

(33 citation statements)

References 26 publications

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“…[12]. Different kind of (nonnormalized) para-Grassmann 'left' CS for finite level pseudo-Hermitian systems are considered in [14,15].…”

Section: Resultsmentioning

confidence: 99%

“…Following the scheme developed in section 3 (and in [16] for Hermitian case) one can construct bi-overcomplete 'left' and 'right' ladder operator eigenstates for a(n; ρ) and b † (n; ρ) using the para-Grassmann algebra (7) and the integration rules (13). Bi-overcomplete sets of para-Grassmann 'left' (nonnormalized) eigenstates of a(n; ρ) and b † (n; ρ) were constructed in [14] using different paragrassmannian variables and integration rules. In [15] overcomplete families of eigenstates of a ′ = q N/2 a(n; ρ (q) ) (where, in our notations, [[N ]] = b(n; ρ (q) )a(n; ρ (q) )) and c ′ = q N ′ /2 b † (n; ρ (q) ) (where [[N ′ ]] = a † (n; ρ (q) ) b † (n; ρ (q) ) are built up using also different paragrassmannian variables and integration rules.…”

Section: N-pf and Non-hermitian Systemsmentioning

confidence: 99%

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Nonlinearn-pseudo fermions

Trifonov¹

2012

J. Phys. A: Math. Theor.

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Nonlinear pseudo-fermions of degree n (n-pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators a and b, b = a † , obeying the simple nonlinear anticommutation relation ab + b n a n = 1. The (n + 1)-order nilpotency of these operators follows from the existence of unique (up to a bi-normalization factor) avacuum. Supposing appropriate (n + 1)-order nilpotent para-Grassmann variables and integration rules the sets of n-pseudo-fermion number states, and 'right' and 'left' ladder operator bi-overcomplete sets of coherent states are constructed. Explicit examples of n-pseudo-fermion ladder operators are provided, and the relation of pseudo-fermions to finite-level pseudo-Hermitian systems is briefly considered.

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“…[12]. Different kind of (nonnormalized) para-Grassmann 'left' CS for finite level pseudo-Hermitian systems are considered in [14,15].…”

Section: Resultsmentioning

confidence: 99%

Section: N-pf and Non-hermitian Systemsmentioning

confidence: 99%

Nonlinearn-pseudo fermions

Trifonov¹

2012

J. Phys. A: Math. Theor.

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“…We not that in [25] the creation operator b ♯ is η-pseudo-Hermitian adjoint of the annihilation operator b, but our changed ladder operatorb is not η-pseudo-Hermitian adjoint of b, and we have b ♯ =bq −N . One could easily check that the pseudo-Hermitian number states can be expressed in terms of b andb (also c andc for the dual space), and these operators annihilate and create the number states as follows…”

Section: )mentioning

confidence: 87%

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

Maleki¹

2011

SIGMA

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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.

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“…We say that the three operators A(n), A † (n) and N , satisfying (1) and (14) form the nfermion algebra. At n = 1 it coincides with the (standard) fermion algebra.…”

Section: Nonlinear Fermion Algebra and Fock Statesmentioning

confidence: 99%

Nonlinear fermions and coherent states

Trifonov¹

2012

J. Phys. A: Math. Theor.

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Nonlinear fermions of degree n (n-fermions) are introduced as particles with creation and annihilation operators obeying the simple nonlinear anticommutation relation AA † + A † n A n = 1. The (n + 1)-order nilpotency of these operators follows from the existence of unique A-vacuum. Supposing appropreate (n + 1)-order nilpotent paraGrassmann variables and integration rules the sets of n-fermion number states, 'right' and 'left' ladder operator coherent states (CS) and displacement-operator-like CS are constructed. The (n + 1) × (n + 1) matrix realization of the related para-Grassmann algebra is provided. General (n+1)-order nilpotent ladder operators of finite dimensional systems are expressed as polynomials in terms of n-fermion operators. Overcomplete sets of (normalized) 'right' and 'left' eigenstates of such general ladder operators are constructed and their properties briefly discussed.

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Generalized Grassmannian coherent states for pseudo-Hermitiann-level systems

Cited by 13 publications

References 26 publications

Nonlinearn-pseudo fermions

Nonlinearn-pseudo fermions

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

Nonlinear fermions and coherent states

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