Paths of zeros of analytic functions describing finite quantum systems

TL;DR

This paper investigates the trajectories of zeros of analytic functions representing finite quantum systems, introducing a semi-analytic method to compute these paths and analyzing their behavior in periodic systems through numerical examples.

Contribution

It presents a semi-analytic approach to calculate zero paths in finite quantum systems and provides detailed analysis for periodic cases.

Findings

Paths of zeros describe quantum system evolution

Semi-analytic method effectively computes zero trajectories

Numerical examples illustrate theoretical concepts

Abstract

Quantum systems with positions and momenta in 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.