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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Variational Gaussian wave packets revisited - Chri
stian Lubich (Eberhard Karls UniversitÃ¤t TÃ¼bingen)
DTSTART;TZID=Europe/London:20190709T150000
DTEND;TZID=Europe/London:20190709T160000
UID:TALK127045AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/127045
DESCRIPTION:The talk reviews Gaussian wave packets that evolve
according to the Dirac-Frenkel time-dependent var
iational principle for the semi-classically scaled
Schr\\"odinger equation. Old and new results on t
he approximation 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 new error bound for averages of observables
with a Weyl symbol\, which shows the double approx
imation order in the semi-classical scaling parame
ter in comparison with the norm estimate.

The variational equations of motion in Hagedorn&#
39\;s parametrization of the Gaussian are presente
d. They show a perfect quantum-classical correspon
dence and allow us to read off directly that the E
hrenfest time is determined by the Lyapunov expone
nt of the classical equations of motion.

A variational splitting integrator is formulated
and its remarkable conservation and approximation
properties are discussed. A new result shows that
the integrator approximates averages of observabl
es with the full order in the time stepsize\, with
an error constant that is uniform in the semiclas
sical parameter.

The material presented
here for variational Gaussians is part of an Acta
Numerica review article on computational methods f
or quantum dynamics in the semi-classical regime\,
which is currently in preparation in joint work w
ith Caroline Lasser.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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