Nonadiabatic dynamics in semiquantal physics

Abstract

Every physical regime is some sort of approximation of reality. One lesserknown realm that is the semiquantal regime, which may be used to describe systems with both classical and quantum subcomponents. In the present review, we discuss nonadiabatic dynamics in the semiquantal regime. Our primary concern is electronic-nuclear coupling in polyatomic molecules, but we discuss several other situations as well. We begin our presentation by formulating the semiquantal approximation in quantum systems with degrees-1 of-freedom that evolve at different speeds. We discuss nonadiabatic phenomena, focusing on their relation to the Born-Oppenheimer approximation.We present several examples-including Jahn-Teller distortion in molecules and crystals and the dynamics of solvated electrons, buckyballs, nanotubes, atoms in a resonant cavity, SQUIDs, quantum particle-spin systems, and micromasers. We also highlight vibrating quantum billiards as a useful abstraction of semiquantal dynamics. PAC NOS 03.65.Sq, 02.70.Ns, 05.45.Mt

Non-Linear Semi-Quantum Hamiltonians and Its Associated Lie Algebras

“…Thus, the Hamiltonian representing a semi-quantum system may be expressed in the form given by Equation (1) [20]) because they can be thought of as quantum billiards in which a quantum particle of mass m , confined in a potential well ( ) V q (generated by a classical mass M ) undergoes elastic interactions [20] [23]. Accordingly, the classical part of Hamiltonian given by Equation (15) has the form ( )…”

“…Let us consider a mixed physical system represented by the semiquantum Hamiltonian represented by Equation (15) with a coupling term [1] [12] [20] [24]- [26]. As the classical degrees of freedom act like as if they were parameters, the Hamiltonian given by Equation (15) may be cast as [3] [23] ( ) ( ) freedom.…”

“…Thus, the equation of motion for the density operator (9) has been converted into a set of coupled Equation (20). Nevertheless, there exist a difference with respect to the full quantum case of [4]: while the set of Equation (11) …”

Uncertainty Principle and Bifurcations in the SU(2) Nonlinear Semiquantum Dynamics

“…One finds in [1] an exhaustive compilation of physical phenomena and technological applications successfully modeled by SD. It is also possible to encounter situations in which SD is used to describe physical phenomena [2] [3] [4] [5].…”

Difficulties in Evaluating Lyapunov Exponents for Lie Governed Dynamics

“…Consider a system that possesses both quantum and classic degrees of freedom, with a coupling amongst them, that we call semiquantum [3,[6][7][8][9][10]. The associated Hamiltonian is of the general form [11]…”