Fermionic coherent states for pseudo-Hermitian two-level systems

Abstract

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.

13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs added

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Cited by in corpus (17)

• Linear Pseudo-fermions
• $(H,\rho )$--induced dynamics and large time behaviors
• Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Bi-squeezed states arising from pseudo-bosons
• Generalized Grassmannian Coherent States For Pseudo-Hermitian $n$ Level Systems
• A concise review on pseudo-bosons, pseudo-fermions and their relatives
• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• Damping and Pseudo-fermions
• Non self-adjoint Hamiltonians with complex eigenvalues
• Topological decompositions of the Pauli group and their influence on dynamical systems
• Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
• On the Pauli group on 2-qubits in dynamical systems with pseudofermions
• Nonlinear n-Pseudo Fermions
• Generalized Grassmann variables for quantum kit (k-level) systems and Barut-Girardello coherent states for su(r+1) algebras
• Pseudo-Hermitian systems, involutive symmetries and pseudofermions
• Fermion Coherence Hamiltonians