Local Measure of Quantum Effects in Quantum Dynamics

The
Madelung–de Broglie–Bohm formulation of the Schrödinger
equation casts the time-evolution of a wave function as dynamics of
an ensemble of quantum, or Bohmian, trajectories, interacting via
the nonlocal quantum potential. This trajectory perspective gives
insight into the quantumness (or classicality) of a given system due
to clear partitioning of the energy into classical and quantum components.
Here, we propose a system-independent measure of the quantumness of
dynamics, based on the energy time-change, referred to as “quantum
power”. This measure is local in the coordinate space. Based
on applications to model chemical systems, we argue that during the
transition from the quantum to classical regime, defined as compression
of quantization, the quantum features in dynamics do not “disappear”
but are pushed forward in time. This feature may be used to gauge
the validity of the semiclassical and other approximate dynamics approaches
in applications to anharmonic systems.