One dimensional directed polymer "memory model"

TL;DR

This paper introduces a simple statistical memory model for one-dimensional directed polymers that can store and retrieve specific trajectories, with analysis of overlap based on temperature and potential strength.

Contribution

It proposes a novel memory model for directed polymers using an elastic string Hamiltonian with local attraction, enabling trajectory storage and retrieval.

Findings

Overlap depends on temperature and potential strength

Model effectively stores and retrieves quenched trajectories

Provides analytical expressions for average overlap

Abstract

In this paper I propose very simple statistical "memory model" of one-dimensional directed polymers which is capable to store and retrieve a given random quenched trajectory. The model is defined in terms of the elastic string Hamiltonian with the local attractive potential between the dynamic and the quenched random strings. The average overlap between them is calculated as a function of the temperature and the strength of the attractive potential.