Fermion Coherence Hamiltonians

Abstract

We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence Hamiltonian, which is of the more general form of the nonstationary forced bosonic oscillator. If however one admits Grassmann variables as Hamiltonian parameters then the coherence Hamiltonian takes again the form of (Grassmannian fermionic) forced oscillator.Comment: latex, 10 pages, no figure

Nonlinear fermions and coherent states

“…In the last decades or so, considerable attention has been paid in the literature to the problems of extension and adoption of the celebrated coherent state (CS) method [1][2][3] for description of quantum systems with finite-dimensional Hilbert state space-fermionic [4][5][6], parafermionic (k-fermionic) [7][8][9][10] and parabosonic [11], Hermitian and pseudo-Hermitian [12][13][14][15][16], systems with discrete finite coordinate spectra [17,18]. Finite-dimensional quantum mechanics is proved useful in many areas, such as quantum computing, quantum optics, signal analysis etc (see e.g.…”

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

“…In this study, we discuss the isotonic oscillator with a non-polynomial term which is a Hermitian counterpart of non-Hermitian Swanson Hamiltonian [22][23][24][25][26][27][28][29]; in other words, our model can be a generalization of the non-Hermitian models for a nonlinear isotonic potential within the framework of pseudo-supersymmetry [30][31][32]. We shall also seek the solutions of the corresponding system.…”