Quantum dynamics in nanoscale magnets in dissipative environments

In discrete energy structure of nanoscale magnets, nonadiabatic transitions at avoided level crossings lead to fundamental processes of dynamics of magnetizations. The thermal environment causes dissipative effects on these processes. In this paper we review the features of the nonadiabatic transition and the influence of the thermal environment. In particular we discuss the temperature independent stepwise structure of magnetization at very low temperatures (deceptive nonadiabatic transition), the alternate enhancement of relaxation in the sequence of resonant tunneling points (parity effects), and processes caused by combinations of nonadiabatic transitions and disturbance due to external noises