Type: Seminar

Distribution: World

Expiry: 24 Nov 2015

Auth: olver@p624.pc (assumed)

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 SchrÃ¶dinger 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 â€“ quantum tunnelling and quantum scattering â€“ and their computation and, time allowing, discuss an extension of this methodology to time-dependent semiclassical systems using Magnus expansions.