Maximal estimates for the Schrödinger equation with orthonormal initial data

Abstract

For the one-dimensional Schrodinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates generalize a classical result of Kenig–Ponce–Vega and allow us to obtain pointwise convergence results associated with systems of infinitely many fermions. The maximal-in-space estimates simultaneously address an endpoint problem raised by Frank–Sabin in their work on Strichartz estimates for orthonormal systems of data, and provide a path toward proving our maximal-in-time estimates.