Generalized Grassmannian Coherent States For Pseudo-Hermitian nn Level Systems

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 $SU_{q}(2)$ for three level pseudo-Hermitian system are presented.Comment: 17 page

Invariants and Coherent States for Nonstationary Fermionic Forced Oscillator

The most general form of Hamiltonian that preserves fermionic coherent states stable in time is found in the form of nonstationary fermion oscillator. Invariant creation and annihilation operators and related Fock states and coherent states are built up for the more general system of nonstationary forced fermion oscillator.Comment: 13 pages, Latex, no figure

Fermionic coherent states for pseudo-Hermitian two-level systems

We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators the two-level system' Hamiltonian takes a factorized form similar to that of a harmonic oscillator.Comment: 13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs adde

Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry

Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag 2}, where $\alpha \neq \beta$ and $\xi$ is a first order differential operator, to obtain the partner potentials $V_{+}(x)$ and $V_{-}(x)$ which are new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian equivalents of the non-Hermitian partner Hamiltonians $H_{\pm}$. We have provided an algebraic way to obtain the spectrum and wavefunctions of a nonlinear isotonic oscillator. The solutions of $V_{-}(x)$ which are Hermitian counterparts of Swanson Hamiltonian are obtained under some parameter restrictions that are found. Also, we have checked that if the intertwining operator satisfies $\eta_{1} H_{-}=H_{+} \eta_{1}$, where $\eta_{1}=\rho^{-1} \mathcal{A} \rho$ and $\mathcal{A}$ is the first order differential operator, which factorizes Hermitian equivalents of $H_{\pm}$.Comment: 11 page

Evolution of Grassmannian invariant-angle coherent states and nonadiabatic Hannay's angle

We show how the exact evolution and nonadiabatic Hannay's angle of Grassmannian classical mechanics of spin one half in a varying external magnetic field is associated with the evolution of Grassmannian invariant-angle coherent states