## Computer simulation of nonadiabatic dynamics by means of the quantum-classical Liouville equation.

##### Abstract

Simulation of quantum dynamics for many-body systems is an open area of research.
For interacting many-body quantum systems, the computer memory necessary
to perform calculations has an astronomical value, so that approximated models
are needed to reduce the required computational resources. A useful approximation
that can often be made is that of quantum-classical dynamics, where the majority of
the degrees are treated classically, while a few of them must be treated quantum mechanically.
When energy is exchanged very quickly between the quantum subsystem
and classical environment, the dynamics is nonadiabatic. Most theories for nonadiabatic
dynamics are unsatisfactory, as they fail to properly describe the quantum
backreaction of the subsystem on the environment. However, an approach based on
the quantum-classical Liouville equation solves this problem. Even so, nonadiabatic
dynamics is di cult to implement on a computer, and longer simulation times are
often inaccessible due to statistical error. There is thus a need for improved algorithms
for nonadiabatic dynamics. In this thesis, two algorithms that utilise the
quantum-classical Liouville equation will be qualitatively and quantitatively compared.
In addition, stochastic sampling schemes for nonadiabatic transitions will
be studied, and a new sampling scheme is introduced [D. A. Uken et al., Phys.
Rev. E. 88, 033301 (2013)] which proves to have a dramatic advantage over existing
techniques, allowing far longer simulation times to be calculated reliably.