The orthonormal Strichartz inequality on torus

TL;DR

This paper establishes sharp orthonormal system Strichartz inequalities on the torus and applies them to prove well-posedness for the periodic Hartree equation involving infinitely many quantum particles.

Contribution

It introduces sharp orthonormal system Strichartz inequalities on the torus and demonstrates their application to quantum many-body problems.

Findings

Sharp estimates for orthonormal system Strichartz inequalities on the torus.

Application to well-posedness of the periodic Hartree equation.

Extension of recent works by Frank-Lewin-Lieb-Seiringer and Frank-Sabin.

Abstract

In this paper, motivated by recent important works due to Frank-Lewin-Lieb-Seiringer \cite{FLLS} and Frank-Sabin \cite{frank-sabin-1}, we study the Strichartz inequality on torus with the orthonormal system input and obtain sharp estimates in certain sense. An application of the inequality shows the well-posedness to the periodic Hartree equation describing the infinitely many quantum particles with the power type interaction.