On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schr\"odinger hierarchy

TL;DR

This paper proves the unconditional uniqueness of solutions to an infinite hierarchy of nonlinear PDEs describing the limiting dynamics of infinitely many interacting anyons in two dimensions, extending previous linear hierarchy results.

Contribution

It establishes the first unconditional uniqueness result for the nonlinear IRCSS hierarchy, linking it directly to the Chern-Simons-Schr"odinger system.

Findings

Uniqueness of solutions to the IRCSS hierarchy in 2D.

Implication of uniqueness for the Chern-Simons-Schr"odinger system.

Extension from linear to nonlinear hierarchy analysis.

Abstract

In this article we establish the unconditional uniqueness of solutions to an Infinite Radial Chern-Simons-Schr\"odinger (IRCSS) hierarchy in two spatial dimensions. The IRCSS hierarchy is a system of infinitely many coupled PDEs that describes the limiting Chern-Simons-Schr\"odinger dynamics of infinitely many interacting anyons. The anyons are two dimensional objects which interact through a self-generated field. Due to the interactions with the self-generated field, the IRCSS hierarchy is a system of nonlinear PDEs, which distinguishes it from the linear infinite hierarchies studied previously. Factorized solutions of the IRCSS hierarchy are determined by solutions of the Chern-Simons-Schr\"odinger system. Our result therefore implies the unconditional uniqueness of solutions to the radial Chern-Simons-Schr\"odinger system as well.