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.

arXiv commentAMS Latex, 31 pages. Minor typos fixed

References in corpus (10)

• Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Mean-field Evolution of Fermionic Systems
• Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti
• The Hartree equation for infinitely many particles. I. Well-posedness theory
• Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons
• The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in $d=3$ based on spacetime norms
• Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy
• A positive density analogue of the Lieb-Thirring inequality

Cited by in corpus (6)

• The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states
• Long-time behaviour of time-dependent density functional theory
• Asymptotic stability of a wide class of stationary solutions for the Hartree and Schrödinger equations for infinitely many particles
• Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction
• 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