Real time scale simulation for quantum processes in dissipative environments

Nanoscale magnets show the dynamics of magnetization responding time-dependent external fields. If the field changes faster than the time scale of the system, the system cannot follow the change of the field and it shows the so-called non-adiabatic process. On the other hand, if the change of the field is slow, the system follows the change adiabatically. However, if the change is too slow, the environment causes the thermalization and the system shows additional characteristics, e.g. the phonon-bottleneck process in V15 and magnetization process of Fe-rings, such as Pe12, etc. In order to study such cases numerically, we have to simulate very long time comparing with the precession period of the magnetization. We will present a new method to study dissipative processes for long time. With this method we will clarify characteristics of dynamics of nanoscale molecular magnets.