Population Dynamics and Non-Hermitian Localization

Details Population Dynamics and Non-Hermitian Localization Population Dynamics and Non-Hermitian Localization

1999-03-18

arxiv.org/abs/cond-mat/9903276v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 11 figures

Scientific paper

10.1007/BFb0105012

We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the Schroedinger-like operator which appears in linearized growth models. We illustrate the basic ideas by reviewing how convection affects the evolution of a population influenced by a simple square well growth profile. Results from discrete lattice growth models in both one and two dimensions are presented. A set of similarity transformations which lead to exact results for the spectrum and winding numbers of eigenfunctions for random growth rates in one dimension is described in detail. We discuss the influence of boundary conditions, and argue that periodic boundary conditions lead to results which are in fact typical of a broad class of growth problems with convection.

Affiliated with

Also associated with

No associations

Rating

Population Dynamics and Non-Hermitian Localization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Population Dynamics and Non-Hermitian Localization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Population Dynamics and Non-Hermitian Localization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-394749