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

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.

AMS Latex, 31 pages. Minor typos fixed

References in corpus (2)

• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy

Cited by in corpus (6)

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• Probabilistic Strichartz estimates in Schatten classes and their applications to the Hartree equation
• Stability of homogeneous equilibria of the Hartree-Fock equation, for its equivalent formulation for random fields