Derivation of an effective evolution equation for a strongly coupled polaron

Frank, Rupert L.; Zhou, Gang

doi:10.2140/apde.2017.10.379

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Derivation of an effective evolution equation for a strongly coupled polaron

Rupert L. Frank and Zhou Gang

Vol. 10 (2017), No. 2, 379–422

DOI: 10.2140/apde.2017.10.379

Abstract

Fröhlich’s polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron are approximated by an effective nonlinear partial differential equation due to Landau and Pekar, in which the phonon field is treated as a classical field.

Keywords

polaron, dynamics, quantized field

Mathematical Subject Classification 2010

Primary: 35Q40, 46N50

Milestones

Received: 30 June 2016

Accepted: 28 November 2016

Published: 23 February 2017

Authors

Rupert L. Frank
Mathematics 253-37 Caltech Pasadena, CA 91125 United States

Zhou Gang
Mathematics 253-37 Caltech Pasadena, CA 91125 United States

Vol. 10, No. 2, 2017