Communications in Mathematical Sciences
Volume 15 (2017)
Averaging of nonlinear Schrödinger equations with strong magnetic confinement
Pages: 1933 – 1945
We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the Landau Hamiltonian. Using an averaging technique we derive an associated effective description via an averaged model of nonlinear Schrödinger type. In a special case this also yields a derivation of the LLL equation.
nonlinear Schrödinger equation, magnetic confinement, Landau levels, averaging
2010 Mathematics Subject Classification
R.L.F. has been supported by the U.S. National Science Foundation through grant no. DMS-1363432.
F.M. acknowledges support by the ANR project Moonrise ANR-14-CE23-0007-01.
C.S. has been supported by the U.S. National Science Foundation through grant no. DMS-1348092.
Received 15 March 2017
Accepted 30 June 2017
Published 16 October 2017