Vol. 10, No. 2, 2017

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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
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