Quantum dynamics in classical constant-temperature baths.
In this dissertation the formulation of various integration algorithms is studied, with a view to simulate quantum-classical systems in contact with a thermal bath. In particular focus is given to the constant temperature dynamics of the Nos e-Hoover, Nos e-Hoover Chain and Nos e-Hoover Power thermostat schemes. Through the use of the time symmetric Trotter factorisation of the Liouville operator, algorithms are derived that are both time-reversible and measure-preserving. The efficiency of these algorithms is tested via the constant temperature simulation of a low-dimensional harmonic system. In addition The Nos e-Hoover Power thermostat was then extended to the quantum-classical case. The damping of a tunnelling spin coupled to a thermalised harmonic mode was simulated and the results are presented.