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Paths of zeros of analytic functions of finite quantum systems using various types of matrices

Evangelides P, Talias M

We consider quantum systems in d dimensional Hilbert space using a computational approach. We focus on a specific analytic representation in a cell S which describes the finite quantum system. The time evolution of the system produces d paths of zeros. The central notion is to restrict our attention to matrices such as: Vandermonde and Banded instead of any periodic Hamiltonian matrix. In particular we provide numerical examples of interesting closed paths of the zeros. In this paper we use an efficient numerical approach to generate the paths of zeros based on specific categories of matrices