Population dynamics and semiclassical methods

Abstract

We intend to develop models in population dynamics describing speciation mechanisms compatible with observed data of abundance and diversity. In particular, we will improve the model we previously developed, introducing more realistic characteristics, like geographical barriers and natural selection, in order to understand how these ingredients contribute and modify the abundance distributions in the species generated. In the area of semiclassical methods we are developing a new semiclassical expression for the coherent state propagator based on an initial value representation. This new formula avoids the critical problem of search for appropriate complex trajectories exiting in the current approximations and also removes the unphysical divergences at the so called focal points. We hope this new method will allow the calculation of semiclassical dynamics for systems with many degrees of freedom, something not possible today. (AU)