Global Well-posedness of the NLS System for infinitely many fermions

TL;DR

This paper proves the global well-posedness of the nonlinear Schrödinger system modeling infinitely many fermions with delta interactions, extending previous results to less regular interactions in two and three dimensions.

Contribution

It establishes the global existence and uniqueness of solutions for the fermionic NLS system with delta pair interactions, broadening the scope of prior regular interaction results.

Findings

Proves global well-posedness for the fermionic NLS system in 2D and 3D.

Extends previous results to delta (less regular) pair interactions.

Analyzes quantum fluctuation dynamics near the Fermi sea at zero temperature.

Abstract

In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions $d=2,3$, and prove global well-posedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by M. Lewin and J. Sabin, who addressed this problem for more regular pair interactions.