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TZID:Europe/Paris
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BEGIN:VEVENT
UID:0-648@lptms.universite-paris-saclay.fr
DTSTART:20181218T110000Z
DTEND:20181218T120000Z
DTSTAMP:20181207T111312Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-christophe-texier-2/
SUMMARY:Séminaire du LPTMS: Christophe Texier - LPTMS\, salle 201\, 2ème 
 étage\, Bât 100\, Campus d'Orsay - 18 Déc 18 11:00
DESCRIPTION:Counting the equilibria of a directed polymer in a random mediu
 m and Anderson localisation\nChristophe Texier (LPTMS\, Université Paris-
 Sud)\nI will discuss a new connection between two different problems: the 
 counting of equilibria of a directed polymer in a random medium (DPRM) and
  the problem of Anderson localisation for the 1D Schrödinger equation. Us
 ing the Kac-Rice formula\, it is possible to express the mean number of eq
 uilibria of a DPRM in terms of functional determinants. In the one-dimensi
 onal situation\, these functional determinants can be calculated thanks to
  the Gelfand-Yaglom method\, showing that the mean number of equilibria of
  the DPRM growth exponentially with the length of the polymer\, with a rat
 e controlled by the generalized Lyapunov exponent (GLE) of the localisatio
 n problem (cumulant generating function of the log of the wave function). 
 The GLE is solution of a spectral problem studied by combining numerical a
 pproaches and WKB-like approximation. Furthermore\, the formalism can be e
 xtended in order to obtain the number of equilibria at fixed energy\, prov
 iding the (annealed) distribution of the energy density of the line over t
 he equilibria.\n\nReference:\n\n 	Yan V. Fyodorov\, Pierre Le Doussal\, Al
 berto Rosso and Christophe Texier\, Exponential number of equilibria and d
 epinning threshold for a directed polymer in a random potential\, Annals o
 f Physics 397\, 1-64 (2018)\n
CATEGORIES:seminars
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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