Multipolarons in a Constant Magnetic Field

• Published in: Annales Henri Poincaré Vol. 15; no. 6; pp. 1037 - 1059
• Main Authors: Anapolitanos, Ioannis, Griesemer, Marcel
• Format: Journal Article
• Language: English
• Published: Basel Springer Basel 01.06.2014
• Subjects: Classical and Quantum Gravitation; Dynamical Systems and Ergodic Theory; Elementary Particles; Mathematical and Computational Physics; Mathematical Methods in Physics; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Relativity Theory; Theoretical; Lagrange Equation; Quartic Term; Essential Spectrum; Magnetic Translation; Operator Inequality
• ISSN: 1424-0637; 1424-0661
• DOI: 10.1007/s00023-013-0266-4

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 term 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 α N , 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 R 3 N .