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SUMMARY:Numerical renormalization group-based approach to secular perturba
 tion theory - Jose Tomas Galvez Ghersi (CITA)
DTSTART:20220128T130000Z
DTEND:20220128T140000Z
UID:TALK167171@talks.cam.ac.uk
CONTACT:Justin Ripley
DESCRIPTION:Perturbation theory is a crucial tool for many physical system
 s\, when exact solutions are not available\, or nonperturbative numerical 
 solutions are intractable. Naive perturbation theory often fails on long t
 imescales\, leading to secularly growing solutions. These divergences have
  been treated with a variety of techniques\, including the powerful dynami
 cal renormalization group (DRG). Most of the existing DRG approaches rely 
 on having analytic solutions up to some order in perturbation theory. Howe
 ver\, sometimes the equations can only be solved numerically. We reformula
 te the DRG in the language of differential geometry\, which allows us to a
 pply it to numerical solutions of the background and perturbation equation
 s. This formulation also enables us to use the DRG in systems with backgro
 und parameter flows\, and therefore\, extend our results to any order in p
 erturbation theory. As an example\, we apply this method to calculate the 
 soliton-like solutions of the Korteweg-de Vries equation deformed by addin
 g a small damping term. We numerically construct DRG solutions which are v
 alid on secular time scales\, long after naive perturbation theory has bro
 ken down.
LOCATION:Zoom
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