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A toy model for scalars in transient magnetic fields. (English) Zbl 1274.85006

Summary: We consider a special magnetic field, as for example the one in the crust of a magnetar, and solve the Klein-Gordon equation describing scalars evolving in such a configuration. For the wave number inside some computable ranges, the amplitude function of the charged boson is very sensitive to the magnetic field induction, turning from oscillatory to exponentially growing modes along Oz. One can recover the periodic behavior characterized by stationary amplitudes, by adding a self-interaction contribution to the spontaneously broken Lagrangian.

MSC:

85A15 Galactic and stellar structure
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
78A25 Electromagnetic theory (general)
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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