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Spectral transition for Dirac operators with electrostatic $δ$-shell potentials supported on the straight line (2107.01156v1)
Published 2 Jul 2021 in math.SP, math-ph, math.AP, and math.MP
Abstract: In this note the two dimensional Dirac operator $A_\eta$ with an electrostatic $\delta$-shell interaction of strength $\eta\in\mathbb R$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths $\eta=\pm 2$ the continuous spectrum of $A_\eta$ inside the spectral gap of the free Dirac operator $A_0$ collapses abruptly to a single point.