High-flux asymptotics for the magnetic Laplacian with uneven field scaling show persistent oscillations when the outer field is fixed, eventual monotonicity for non-circular domains when it grows slowly, and geometry-dependent behavior in the critical regime.
Local strong magnetic fields and the Little-Parks effect
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abstract
Starting from the Ginzburg--Landau model in a planar simply connected domain, with a local compactly supported applied magnetic field, we derive an effective model in the strong field limit, defined on a non-simply connected domain. The effective model features oscillations in the Little-Parks and Aharonov--Bohm spirit. We discuss also a similar question for the lowest eigenvalue of the magnetic Laplacian.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Existence of semiclassical resonances with exponentially small widths near Landau levels for locally constant magnetic fields, and from step discontinuities, wells, or isolated zeros.
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High Flux Asymptotics and Critical Phenomena for the Magnetic Laplacian
High-flux asymptotics for the magnetic Laplacian with uneven field scaling show persistent oscillations when the outer field is fixed, eventual monotonicity for non-circular domains when it grows slowly, and geometry-dependent behavior in the critical regime.
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Semiclassical resonances under local magnetic fields
Existence of semiclassical resonances with exponentially small widths near Landau levels for locally constant magnetic fields, and from step discontinuities, wells, or isolated zeros.