Simple Quantum Dynamics with Thermalization

In this paper, we
introduce two simple quantum dynamics methods.
One is based on the popular surface-hopping method, and the other
is based on rescaling of the propagation on the bath ground-state
potential surface. The first method is special, as it avoids specific
feedback from the simulated quantum system to the bath and can be
applied for precalculated classical trajectories. It is based on the
equipartition theorem to determine if hops between different potential
energy surfaces are allowed. By comparing with the formally exact
Hierarchical Equations Of Motion approach for four model systems we
find that the method generally approximates the quantum dynamics toward
thermal equilibrium very well. The second method is based on rescaling
of the nonadiabatic coupling and also neglect the effect of the state
of the quantum system on the bath. By the nature of the approximations,
they cannot reproduce the effect of bath relaxation following excitation.
However, the methods are both computationally more tractable than
the conventional fewest switches surface hopping, and we foresee that
the methods will be powerful for simulations of quantum dynamics in
systems with complex bath dynamics, where the system–bath coupling
is not too strong compared to the thermal energy.