Localization transition of random copolymers at interfaces

TL;DR

This paper investigates the localization transition of random copolymers at interfaces by mapping the problem onto a quantum ground state problem and introducing a novel variational method for analysis.

Contribution

It introduces a new variational principle for Green's functions to analyze the localization transition of copolymers at interfaces.

Findings

Phase diagram for localization-delocalization transition derived.

Novel variational method for Green's function proposed.

Mapping of copolymer adsorption to quantum ground state problem.

Abstract

We consider adsorption of random copolymer chains onto an interface within the model of Garel et al. Europhysics Letters 8, 9 (1989). By using the replica method the adsorption of the copolymer at the interface is mapped onto the problem of finding the ground state of a quantum mechanical Hamiltonian. To study this ground state we introduce a novel variational principle for the Green's function, which generalizes the well-known Rayleigh-Ritz method of Quantum Mechanics to nonstationary states. Minimization with an appropriate trial Green's function enables us to find the phase diagram for the localization-delocalization transition for an ideal random copolymer at the interface.