University of Connecticut

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Particle, Astrophysics, and Nuclear Physics Seminar

Monday, April 29, 2019
2:00pm – 3:00pm

Storrs Campus
Gant West (Physics Building), P121

Prof. Gerald Dunne, Department of Physics, University of Connecticut

Resurgent Extrapolation: Squeezing Non-Perturbative Information from Perturbation Theory

Extrapolation is an important problem in physics: how to use asymptotic data in one parametric regime to learn about the behavior of a physical function in another parametric regime. For example: extending weak coupling expansions to strong coupling, or high temperature expansions to low temperature, or vice versa. I present new methods from "resurgent asymptotics" that dramatically improve standard numerical procedures for performing such an extrapolation: Borel summation, Pad'e approximants and conformal mapping. I illustrate the method with the concrete example of one of the Painlev'e equations, a class of nonlinear equations with many applications in physics. Starting solely with a finite number of asymptotic coefficients, we obtain a high precision extrapolation of the function throughout the complex plane, even across a phase transition. The precision far exceeds that of state-of-the-art numerical integration methods.


Prof. L. Jin

Physics Department (primary), UConn Master Calendar

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