Invariants and coherent states for a nonstationary fermionic forced oscillator

Abstract

Invariant creation and annihilation operators and related Fock states and coherent states are built up for the system of nonstationary fermionic forced oscillator.

Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States

“…The Hamiltonian (2.1) is the non-Hermitian extension of the Hermitian fermionic Hamiltonian studied in greater detail in our recent work [17]. Due to the nilpotency of the fermionic operators Y and Y † , the Hamiltonian (2.1) which is a linear combination of Y , Y † and (Y † Y − 1 2 ), represents the most general form of such non-Hermitian Hamiltonians.…”

“…The Hamiltonian (2.1) is the non-Hermitian extension of the Hermitian fermionic Hamiltonian studied in greater detail in our recent work [17]. 2 ) close under commutation the su(2) Lie algebra:…”

Fermion Coherence Hamiltonians

“…Thus the fermion coherence Hamiltonian should admit dynamical invariant of the form (invariants of other forms for fermion systems have been considered by Dodonov and Man'ko [7], Abe [2], and Cherbal et al [5])…”

“…The exact evolution of fermion CS |ζ ; t , governed by the more general nonstationary forced oscillator Hamiltonian H f is constructed, using the dynamical invariant ladder operator method [13,16,[22][23][24], in [5],…”

“…Taking then into account that the invariants B(t) and B † (t) have to obey the fermion algebra (15) we derive that [b, B(t)] = 0 if and only if B(t) is proportional to b, B(t) = β ′ (t)b. Thus the fermion coherence Hamiltonian should admit dynamical invariant of the form (Invariants of other forms for fermion systems have been considered by Dodonov and Man'ko [7], Abe [2], and Cherbal et al [5] )…”