1207.2870 (A. Comech et al.)

Polarons as solitary wave solutions to the Dirac-Coulomb system    [PDF]

A. Comech, M. Zubkov

We consider solitary wave solutions to the Dirac-Coulomb system both from physical and mathematical points of view. Possible applications of these solutions in physics are discussed. Namely, we consider the model of Dirac fermions with the Coulomb attraction, which appears in certain condensed matter systems with emergent Dirac fermions interacting via optical phonons. In this model, there exist classical soliton solutions of equations of motion which correspond to polarons. We also discuss the relativistic generalization of this model: the fermion field interacting with the gravitational field, where the Dirac fermions with the Coulomb attraction appear in Newtonian limit. On the mathematical side, we develop analytical methods for the Dirac-Coulomb system, showing that the no-node gap solitons of sufficiently small amplitude are linearly (or spectrally) stable.

View original: http://arxiv.org/abs/1207.2870