Zum Inhalt springen

RMKS Darmstadt 23. Juni 2023

Rhein-Main-Kolloquium

Datum: 23.06.2023

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 

Abstract: 
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.

Referenten

Mark Sellke, Stanford University
Steffen Polzer, Université de Genève

Ort

TU Darmstadt
zoom, Darmstadt

Raum

wird in Kürze bekannt gegeben

Veranstalter

Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381
info(at)stochastik-rhein-mainde


Kooperationspartner

Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

Für diese Veranstaltung ist keine Anmeldung erforderlich. PDF- Link