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Mobile localized solutions for an electron in lattices with dispersive and non-dispersive phonons. (English) Zbl 1364.81239

Summary: We consider a one dimensional lattice in which an electron can interact both with on-site non-dispersive (Einstein) phonons and with longitudinal dispersive acoustic (Debye) phonons. We provide existence conditions for mobile localized electron excitations in the long wave limit. The role of both types of phonon modes on localization is also assessed, together with a discussion of differences existing between the discrete and the continuum approaches. A striking result is that, under certain conditions, localized states can only be stable if they have a non-zero velocity.

MSC:

81V10 Electromagnetic interaction; quantum electrodynamics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

Software:

Matlab; CHARMM
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References:

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