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VERSION:2.0
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PRODID:UW-Madison-Physics-Events
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SEQUENCE:0
UID:UW-Physics-Event-4349
DTSTART:20170223T160000Z
DURATION:PT1H0M0S
DTSTAMP:20260406T031517Z
LAST-MODIFIED:20170221T152443Z
LOCATION:5310 Chamberlin
SUMMARY:Semi-classical limit for the Schrodinger equation with lattice
  potential\, and band-crossing\, R. G. Herb Condensed Matter Seminar\,
  Qin Li \, UW-Madison
DESCRIPTION:In this talk we derive and compute the semi-classical limi
 t of the Schrodinger equation with lattice potential. In [Gerard-Marko
 wich-Mauser-Poupaud\, Comm. Pure Appl. Math. 1997]\, the limit is deri
 ved under the assumption that energy bands are well-separated\, namely
 \, the system is adiabatic. However\, in reality\, this assumption is 
 generically invalid. We remove the assumption\, and obtain a general m
 odel by performing multi-scale variable separation with the Bloch deco
 mposition and the Wigner transformation. Asymptotically this new full 
 system recovers the old one in the adiabatic region. In the computatio
 n\, we decompose the domain into regions depending on the distance to 
 the energy band-crossing points\, and apply associated schemes in diff
 erent regions. A nature extension to the diabatic transition beyond th
 e Born-Oppenheimer approximation will also be given at the end of the 
 talk.
URL:https://www.physics.wisc.edu/events/?id=4349
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