SMS scnews item created by Sheehan Olver at Fri 6 Nov 2015 1658
Type: Seminar
Distribution: World
Expiry: 24 Nov 2015
Calendar1: 23 Nov 2015
CalLoc1: RC-4082, The Red Centre, UNSW
Auth: olver@p624.pc (assumed)

UNSW Computational Maths Seminar: Iserles -- Fast computation of the semiclassical Schrodinger equation

Fast computation of the semiclassical Schrodinger equation 
Speaker: Arieh Iserles
Affiliation: University of Cambridge 
Date: Mon, 23/11/2015 - 11:05am to 11:55am 
Venue: RC-4082, The Red Centre, UNSW 

Abstract: Equations of quantum mechanics in the
semiclassical regime present an enduring challenge for numerical analysts, because their
solution is highly oscillatory and evolves on two scales.  Standard computational
approaches to the semiclassical Schrödinger equation do not allow for long time
integration as required, for example, in quantum control of atoms by short laser
bursts.  This has motivated our approach of asymptotic splittings.  Combining techniques
from Lie-algebra theory and numerical algebra, we present a new computational paradigm
of symmetric Zassenhaus splittings, which lends itself to a very precise discretisation
in long time intervals, at very little cost.  We will illustrate our talk by examples of
quantum phenomena – quantum tunnelling and quantum scattering – and their
computation and, time allowing, discuss an extension of this methodology to
time-dependent semiclassical systems using Magnus expansions.

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