The Gross-Pitaevskii Hierarchy on General Rectangular Tori

Herr S, Sohinger V. The Gross-Pitaevskii Hierarchy on General Rectangular Tori. Archive for Rational Mechanics and Analysis. 2016;220(3):1119-1158.In this work, we study the Gross-Pitaevskii hierarchy on general-rational and irrational-rectangular tori of dimensions two and three. This is a system of infinitely many linear partial differential equations which arises in the rigorous derivation of the nonlinear Schrodinger equation. We prove a conditional uniqueness result for the hierarchy. In two dimensions, this result allows us to obtain a rigorous derivation of the defocusing cubic nonlinear Schrodinger equation from the dynamics of many-body quantum systems. On irrational tori, this question was posed as an open problem in the previous work of Kirkpatrick, Schlein, and Staffilani