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Averaging of nonlinear Schrödinger equations with strong magnetic confinement. (English) Zbl 1387.35549

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B25 Singular perturbations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q40 PDEs in connection with quantum mechanics
35R09 Integro-partial differential equations
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