Fermion Coherence Hamiltonians

TL;DR

This paper characterizes the most general Hamiltonian form that maintains fermionic coherent states over time, revealing a unique structure akin to the nonstationary free fermionic oscillator, with extensions involving Grassmann variables.

Contribution

It identifies the specific form of Hamiltonians that preserve fermionic coherent states and compares it with bosonic cases, introducing Grassmann variables as Hamiltonian parameters.

Findings

Fermionic coherence Hamiltonians are equivalent to nonstationary free fermionic oscillators.

Inclusion of Grassmann variables leads to a Grassmannian forced oscillator form.

Comparison with bosonic coherence Hamiltonians highlights structural differences.

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.