Paths of zeros of analytic functions describing finite quantum systems

• Study of zeros of analytic representations of finite quantum systems.
• Time evolution is described with d paths of zeros.
• Study of zeros of periodic systems.
• Paths of zeros with displacement operators as time evolution operators.

Quantum systems with positions and momenta in Z(d)Z(d) are described by the d zeros of analytic functions on a torus. The d paths of these zeros on the torus describe the time evolution of the system. A semi-analytic method for the calculation of these paths of the zeros is discussed. Detailed analysis of the paths for periodic systems is presented. A periodic system which has the displacement operator to a real power t, as time evolution operator, is studied. Several numerical examples, which elucidate these ideas, are presented.