Generalized Grassmannian Coherent States For Pseudo-Hermitian $n$ Level Systems

Abstract

The purpose of this paper is to generalize fermionic coherent states for two-level systems described by pseudo-Hermitian Hamiltonian \cite{Trifonov}, to n-level systems. Central to this task is the expression of the coherent states in terms of generalized Grassmann variables. These kind of Grassmann coherent states satisfy bi-overcompleteness condition instead of over-completeness one, as it is reasonably expected because of the biorthonormality of the system. Choosing an appropriate Grassmann weight function resolution of identity is examined. Moreover Grassmannian coherent and squeezed states of deformed group $S{U}_q(2)$ for three level pseudo-Hermitian system are presented.

17 pages

References in corpus (3)

• Fermionic coherent states for pseudo-Hermitian two-level systems
• Alternative descriptions and bipartite compound quantum systems
• Coherent states of non-Hermitian quantum systems

Cited by in corpus (5)

• Non linear pseudo-bosons versus hidden Hermiticity
• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems
• Nonlinear n-Pseudo Fermions
• Generalized Grassmann variables for quantum kit (k-level) systems and Barut-Girardello coherent states for su(r+1) algebras