RMKS Darmstadt 23. Juni 2023
Zeit: 15:15–18:00 Uhr
Steffen Polzer (Geneva)
Title: Renewal approach for the energy-momentum relation of the Polaron
Abstract: The Fröhlich polaron is a model for the interaction of an electron with a polar crystal. We study the energy-momentum relation E(P) which is the bottom of the spectrum of the fixed total momentum Hamiltonian H(P). An application of the Feynman-Kac formula leads to Brownian motion perturbed by a pair potential. The point process representation introduced by Mukherjee and Varadhan represents this path measure as a mixture of Gaussian measures, the respective mixing measure can be interpreted in terms of a perturbed birth and death process. We apply the renewal structure of this point process representation in order to obtain a representation of a diagonal element of the resolvent of H(P). This then yields several properties of the energy-momentum relation, such as monotonicity in |P| and that the correction to the quasi-particle energy is negative. Additionally, we will briefly discuss how the point process representation can be applied in order to derive a lower bound for the effective mass of the Polaron.
Mark Sellke (Princeton / Amazon)
Title: The Polaron's Effective Mass and the Gaussian Correlation Inequality
The Fröhlich polaron is a quantum field theoretic model for an electron moving through a crystal lattice. We study its effective mass at large coupling strength, and give a new lower bound matching the quartic growth rate predicted by Landau-Pekar in 1948 up to logarithmic factors. Our approach uses the probabilistic path integral formulation of the problem and takes a high-dimensional geometric viewpoint. In particular we make crucial, systematic use of Royen's Gaussian correlation inequality to exploit the quasi-concavity of the interaction terms.
- TU Darmstadt S2|04 Raum 213
- Hochschulstr. 8, 64289 Darmstadt
S2|04 Raum 213
Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz