Self-localization of directed polymers and oppressive population control

TL;DR

This paper develops a phenomenological theory for the self-localization behavior of directed polymers across different dimensions and maps these findings to population dynamics, revealing phase transitions and novel wave phenomena.

Contribution

It introduces a new theoretical framework for polymer self-localization and connects it to population models, highlighting phase transitions and dynamic behaviors.

Findings

Polymer always self-localizes in 1D.

Phase transition between localized and free states in 2D.

Observation of a pseudo-travelling wave in certain parameters.

Abstract

We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We also map this system to a model of population dynamics with fixed total population. Our previous results translate to static and expanding population clusters, depending on the birth and death rates. A novel ``pseudo-travelling wave'' is observed in some sectors of parameter space.