Abstract: Every physical regime is some sort of
approximation of reality. One lesser-known 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-of-freedom that
evolve at different speeds. We discuss nonadiabatic phenomena,
focusing on their relation to the Born-ppenheimer 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.
Author's note: One interesting aspect of modeling systems is
how to properly consider more than one physical regime
simultaneously. This can occur as multiple lengthscales and
timescales enter into problems and can cause analytical,
numerical, and conceptual difficulties. Turbulent systems, for
example, exhibit plumes of an astounding array of sizes. See Leo
Kadanoff's recent article in Physics Today for an excellent
qualitative discussion of this phenomenon. A specific example of
this occurs in semiquantum physics, which is one (of many) regimes
that seek to interpolate between classical and quantum physics. It
is relevant when some of a system's degrees-of-freedom are faster
than another so that the slower degree-of-freedom is approximated
as classical. One important class of systems in which this occurs
is molecular systems, whose decomposition of speeds arises from
the fact that nuclei and electrons have masses that differ by
roughly four orders of magnitude. Moreover, this has become
increasingly relevant in recent years, as nanomechanical devices
seek to utilize the interaction between electronic and nuclear
motion. Additionally, whenever one attempts to transit between
multiple physical regimes, philosophical implications of model
reduction become highly relevant.
My paper is a survey article discussing the semiquantum
phenomenon and its applications. It is intended primarily for
non-experts and includes references to more technical work on the
various systems and techniques discussed within. Feel free to
contact me if you'd like to discuss this further.