A Functional Central Limit Theorem for Polaron Path Measures

The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem in this context is the validity of a central limit theorem in infinite volume. We show both the existence of the relevant infinite volume limits and a functional central limit theorem in a generality that includes the Frohlich Polaron for all coupling constants. The proofs are based on an extension of a novel method by Mukherjee and Varadhan. (C) 2022 Courant Institute of Mathematics and Wiley Periodicals LLC.

Automated summary

The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a translation-invariant pair potential. This study addresses the validity of a central limit theorem in infinite volume and shows the existence of relevant infinite volume limits. The results apply to the Frohlich Polaron for all coupling constants.