2012/04/25 by Ioannis Anapolitanos, Anapolitanos, Ioannis, Marcel Griesemer +1
Mathematics · Physics and Astronomy · #49S05 (Secondary) #81V70 (Primary) 35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35Q40 #msc:49S05 #msc:81V70
paper · pdf · doi:10.48550/arxiv.1204.5660
19 pages, fully revised version with stronger results allowing for fermionic, bosonic and boltzonic polarons
arxiv created 2013/01/25 · arxiv updated 2013/01/28
The binding of a system of N polarons subject to a constant magnetic field of strength B is investigated within the Pekar-Tomasevich approximation. In this approximation the energy of N polarons is described in terms of a non-quadratic functional with a quartic term that accounts for the electron-electron self-interaction mediated by phonons. The size of a coupling constant, denoted by α, in front of the quartic is determined by the electronic properties of the crystal under consideration, but in any case it is constrained by 0<α<1. For all values of N and B we find an interval αN,B<α<1 where the N polarons bind in a single cluster described by a minimizer of the Pekar-Tomasevich functional. This minimizer is exponentially localized in the N-particle configuration space \R3N.