Organization of strongly interacting directed polymer liquids in the presence of stringent constraints

TL;DR

This paper studies how impenetrable obstacles affect the structure and energetics of strongly interacting directed polymers, revealing depletion and excess regions with free-energy costs scaling quadratically with density, using a series of transformations.

Contribution

It introduces a novel multi-step transformation approach to analyze strongly interacting directed polymers near obstacles, connecting 3D line liquids to 2D plasma models.

Findings

Regions of polymer depletion and excess near obstacles.

Free-energy cost scales quadratically with polymer density.

Transformations link polymer systems to plasma models.

Abstract

The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in the vicinity of the obstacle, and the associated free-energy cost is found to scale quadratically with the average polymer density. The polymer-polymer interactions are accounted for via a sequence of transformations: from the 3D line liquid to a 2D fluid of Bose particles to a 2D composite fermion fluid and, finally, to a 2D one-component plasma. The results presented here are applicable to a range of systems consisting of noncrossing directed lines.