We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks to a particular radial ansatz, which also allows to provide the exact asymptotic behavior of spinor components. Moreover, those solutions admit a variational characterization as least action critical points of a suitable action functional. We also indicate how the content of the present paper allows to extend our previous results for the massive case [5] to more general nonlinearities.
Weakly localized states for nonlinear Dirac equations
William Borrelli
2018-01-01
Abstract
We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks to a particular radial ansatz, which also allows to provide the exact asymptotic behavior of spinor components. Moreover, those solutions admit a variational characterization as least action critical points of a suitable action functional. We also indicate how the content of the present paper allows to extend our previous results for the massive case [5] to more general nonlinearities.File | Dimensione | Formato | |
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