STUDY OF QUASICLASSICAL DYNAMICS OF TRAPPED IONS USING THE COHERENT STATE FORMALISM AND ASSOCIATED ALGEBRAIC GROUPS

The time dependent variational principle (TDVP) has been applied on coherent state orbits and the Hamilton equations of motion on Kähler (symplectic) manifolds result. The classical Hamilton functions associated to the system are realized as the expected values of the quantum Hamiltonian on symplectic coherent states. The formalism applies to Hamilton functions that are nonlinear in the infinitesimal generators of a dynamical symmetry group (in case of 3D ion traps). Using symplectic coherent states, the explicit classical equations of motion on the unit disk have been obtained for any algebraic model that admits the dynamical group Sp(2,R). The corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical equations of motion. The explicit expression of the quantum and classical Hamilton functions, particularized for combined (Paul and Penning) and ideal Paul traps, are obtained for the first time, taking into consideration the effect of trap electric potential nonlinearities. We also obtain the explicit equations of motion for a combined octupole trap, which represents an original result. A dequantization algorithm results.