Existence in the nonlinear Schr\"odinger equation with bounded magnetic field

TL;DR

This paper investigates the existence of ground state solutions for the nonlinear Schrödinger equation influenced by a general magnetic field, without requiring periodicity, symmetry, or electric fields, expanding understanding of such quantum systems.

Contribution

It establishes ground state existence results for nonlinear Schrödinger equations with arbitrary magnetic fields, removing previous symmetry and periodicity constraints.

Findings

Proves existence of ground states under broad magnetic conditions

Does not assume lattice periodicity or symmetry

Applicable to equations with general external magnetic fields

Abstract

The paper studies existence of ground states for the nonlinear Schr\"odinger equation with a general external magnetic field. In particular, no lattice periodicity or symmetry of the magnetic field, or presence of external electric field is required.