Population dynamics and non-hermitian localization

Karin A Dahmen, David R. Nelson, Nadav M. Shnerb

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 Schrödinger-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.
Original languageAmerican English
Title of host publicationStatistical mechanics of biocomplexity
EditorsD. Reguera, J.M.G. Vilar, J.M. Rubí
PublisherSpringer Berlin Heidelberg
ISBN (Print)978-3-540-48486-8
StatePublished - 1999

Publication series

NameLecture Notes in Physics


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