The parity phenomenon of the Floquet spectra

Coherent states approach to Penning trap

“…Moreover, they become fundamental for the determination of the intrinsic algebraic structure of the involved Hamiltonian (compare equation ( 22)). Observe that some of these properties were found previously for operators imitating the Hamiltonian in non-inertial reference frames [5,6]. By means of this example we have shown that such a property arises as well for Hamiltonians in inertial frames of reference.…”

“…where s j , t j ∈ C, j = 1, 2, 3. We require that the eigenvectors and eigenforms be dual to each other [5,6,13], namely,…”

“…with ⊗ denoting the tensor product. The -expression in (11) allows us to decompose the Heisenberg trajectories as three oscillating modes of frequencies ω j [5,6]. Moreover, it will characterize as well the algebraic structure of the Hamiltonian.…”

“…For years the CS have been derived for plenty of Hamiltonians having either a ground or a top state, and some of them admit a group theoretical construction in which this state is acted on by an appropriate displacement operator [2,4]. However, there exist interesting physical systems for which the Hamiltonians have neither ground nor top state [5,6], but a systematic technique to build up the corresponding CS is required anyway. One of those systems consists of a charged particle in an ideal Penning trap [7,8].…”

Coherent States for the Asymmetric Penning Trap

“…However, there exist interesting physical potentials without a ground state for which the identification of the appropriate annihilation and creation operators is not automatic [10][11][12][13]. The system we are going to address in this work, the asymmetric Penning trap, belongs to this class [14,15].…”