Abstract
Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈E(0)+P 2/2M of the translation invariant system constrained to have momentum P and 2. the mass M of a simple particle in an arbitrary slowly varying external potential, V, described by the nonrelativistic Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.
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Partial financial support by U.S. NSF grant PHY-0965859 (E.H.L.), the Simons Foundation (# 230207, E.H.L.) and the NSERC (R.S.) is gratefully acknowledged.
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Dedicated to Herbert Spohn, a leader in the mathematical study of the polaron, on the occasion of his retirement from T.U. München.
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Lieb, E.H., Seiringer, R. Equivalence of Two Definitions of the Effective Mass of a Polaron. J Stat Phys 154, 51–57 (2014). https://doi.org/10.1007/s10955-013-0791-z
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DOI: https://doi.org/10.1007/s10955-013-0791-z