STUDY OF QUASICLASSICAL DYNAMICS OF TRAPPED IONS USING THE COHERENT STATE FORMALISM AND ASSOCIATED ALGEBRAIC GROUPS BOGDAN M. MIHALCEA Department of Low Temperature Plasma, National R&D Institute for Laser, Plasma and Radiation Physics (INFLPR), Atomis ¸tilor Str. 409, RO-077125, M˘ agurele-Bucharest, Romania, EU E-mail: bogdan.mihalcea@inflpr.ro Received September 9, 2016 Abstract. The time dependent variational principle (TDVP) has been applied on coherent state orbits and the Hamilton equations of motion on K¨ ahler (symplectic) manifolds result. The classical Hamilton functions associated to the system are reali- zed as the expected values of the quantum Hamiltonian on symplectic coherent states. The formalism applies to Hamilton functions that are nonlinear in the infinitesimal ge- nerators 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 cor- responding 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 com- bined (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. Key words: Trapped ion; symplectic coherent states; dynamical symmetry group; nonlinear electromagnetic trap; quasienergy state. PACS: 02.20.-a, 03.65.-w, 37.10.Ty. 1. INTRODUCTION The quantum time-dependent harmonic oscillator (TDHO) is used to describe the dynamics of many physical systems [1–5]. The paper uses recent results from the coherent state formalism developed in [4, 9], and applies it in particular to the study of quantum dynamics of ions confined in 3D ion traps. The time-dependent Schr ¨ odinger equation for harmonic oscillators can be solved when the Hamiltonian is a linear combination of the generators that span the Lie al- gebra associated to the SU(1,1) group [6, 7], using the so-called Peremolov’s gene- ralized coherent states [8, 9]. Quantum dynamics in a 3D RF (Paul) ion trap was characterized by means of coherent states, using time-dependent quantum oscillator equations obtained by separating the axial and radial motion from the Schr¨ odinger Romanian Journal of Physics 62, 113 (2017) v.2.0*2017.7.1#4c1015eb