On the scattering problem for infinitely many fermions in dimensions $d\ge 3$ at positive temperature

Abstract

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d\ge 3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper, and extends the important recent result of M. Lewin and J. Sabin of a similar type for dimension d=2. In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d\ge 3$.

References in corpus (3)

• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti
• A counterexample to an endpoint bilinear Strichartz inequality