Equivalence of Two Definitions of the Effective Mass of a Polaron
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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.
KeywordsPolaron Effective mass Quantum field theory Dressed particle
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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