Product Approximations for a Class of Quantum Anharmonic Oscillators: Analytical and Numerical Results
IIIUL, Room B1-01
2013-07-23 14:30 2013-07-23 15:30 2013-07-23 14:30 .. 15:30
Pierre-A. Vuillermot (Institut Élie Cartan de Lorraine, UMR-CNRS 7502)
In this talk I will present some recent analytical and numerical results obtained jointly with W. P. Petersen regarding a class of non-autonomous Schrödinger equations in one space dimension describing the dynamics of quantum anharmonic oscillators driven by time-dependent quartic interactions. I will do so within a suitably constructed Faedo-Galerkin scheme by analyzing several product approximations for their solutions, which involve several exponential operator splittings. More specifically, the main objective of the talk will be to present results that pertain to the convergence rates and to the accuracy of such approximations, among which there are extensions of the Trotter-Kato product formula and several other variants.