BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Variational Gaussian wave packets revisited - Christian Lubich (Eb
 erhard Karls Universität Tübingen)
DTSTART:20190709T140000Z
DTEND:20190709T150000Z
UID:TALK127045@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The talk reviews Gaussian wave packets that evolve according t
 o the Dirac-Frenkel time-dependent variational principle for the semi-clas
 sically scaled Schr\\"odinger equation. Old and new results on the approxi
 mation to the wave function are given\, in particular an $L^2$ error bound
  that goes back to Hagedorn (1980) in a non-variational setting\, and a ne
 w error bound for averages of observables with a Weyl symbol\, which shows
  the double approximation order in the semi-classical scaling parameter in
  comparison with the norm estimate.<br> <br> The variational equations of 
 motion in Hagedorn&#39\;s parametrization of the Gaussian are presented. T
 hey show a perfect quantum-classical correspondence and allow us to read o
 ff directly that the Ehrenfest time is determined by the Lyapunov exponent
  of the classical equations of motion. <br>  <br> A variational splitting 
 integrator is formulated and its remarkable conservation and approximation
  properties are discussed. A new result shows that the integrator approxim
 ates averages of observables with the full order in the time stepsize\, wi
 th an error constant that is uniform in the semiclassical parameter.<br>  
 <br> The material presented here for variational Gaussians is part of an A
 cta Numerica review article on computational methods for quantum dynamics 
 in the semi-classical regime\, which is currently in preparation in joint 
 work with Caroline Lasser.<br> <br>
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR