Motion of Wavefunction Zeros in Spin-Boson Systems

TL;DR

This paper investigates the dynamics of wavefunction zeros in spin-boson systems using the analytic-Bargmann representation, providing insights into their motion under various Hamiltonians including the Jaynes-Cummings model.

Contribution

It introduces a novel approach to analyze wavefunction zeros' motion in spin-boson systems via a system of equations derived from the Schrödinger equation.

Findings

Zeros follow a non-linear flow in complex space

Numerical solutions illustrate zero dynamics for specific models

Analysis includes both linear and non-linear Hamiltonians

Abstract

In the analytic-Bargmann representation associated with the harmonic oscillator and spin coherent states, the wavefunction as entire complex functions can be factorized in terms of their zeros in a unique way. The Schr\"odinger equation of motion for the wavefunction is turned to a system of equations for its zeros. The motion of these zeros as a non-linear flow of points is studied and interpreted for linear and non-linear bosonic and spin Hamiltonians. Attention is given to the study of the zeros of the Jaynes-Cummings model and to its finite analoque. Numerical solutions are derived and discussed.