Ground States of Fermionic Nonlinear Schrödinger Systems with Coulomb Potential I: The L²-Subcritical Case

2023/10/01 by Bin Chen, Chen, Bin, Yujin Guo +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2310.00563

openalex publication_date 2023/10/01 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28

Abstract

We consider ground states of the N coupled fermionic nonlinear Schrödinger systems with the Coulomb potential V(x) in the L²-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter α>0, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as α→∞, where the mass concentrates at one of the singular points for the Coulomb potential V(x).

Cited by

• Gagliardo-Nirenberg-Sobolev inequalities and ground states of Fermions in relativistic Hartree-Fock model

Related

• Ground States of Fermionic Nonlinear Schrödinger Systems with Coulomb Potential II: The L²-Critical Case
• Hartree-Fock type systems: existence of ground states and asymptotic behavior
• Mass Concentration and Local Uniqueness of Ground States for L²-subcritical Nonlinear Schrödinger Equations
• Ground states for a coupled nonlinear Schrödinger system
• Characterization of ground-states for a system of M coupled semilinear\n Schr "odinger equations and applications