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.
About the speaker:
Professor Arieh Iserles has recently retired from the Chair in the Numerical Solution of Differential Equations at University of Cambridge. He is a world-class numerical analyst with broad interests in numerical differential equations, approximation theory, fast algorithms, applied analysis and the computation of highly oscillatory phenomena. He has published in excess of 200 papers and his textbook, “A First Course in the Numerical Analysis of Differential Equations”, is in wide use worldwide. Arieh Iserles has been awarded the 1999 Lars Onsager Medal, the 2012 David G. Crighton Medal and the 2014 SIAM Prize for Distinguished Service to the Profession. He is the Managing Editor of Acta Numerica, Editor-in-Chief of IMA Journal of Numerical Analysis and an editor of many other journals and book series. Arieh Iserles is a member of EPSRC Strategic Advisory Team for mathematics, Panel PE1 of European Research Council, Physical Sciences Panel of Hong Kong Research Grants Committee and Cambridge University Press Academic Publications Committee. Until a year ago he was the Director of Cambridge Centre for Analysis.
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify Vera Roshchina at RMIT (maths.colloquia@rmit.edu.au) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)