SC 98-29 Wilhelm Huisinga, Lorenzo Pesce, Ronnie Kosloff, Peter Saalfrank: Faber and Newton Polynomial Integrators for Open-System
Density Matrix Propagation Appeared in: J. Chem. Phys. 110 (1999) 12
Abstract: Two polynomial expansions of the time-evolution superoperator
to
directly
integrate Markovian Liouville-von Neumann (LvN) equations for quantum
open systems, namely the Newton interpolation and the Faber approximation, are
presented and critically compared. Details on the numerical
implementation including error control, and on the
performance of either method are given.
In a first physical application,
a damped harmonic oscillator is considered.
Then, the Faber approximation is applied
to compute a condensed phase absorption
spectrum, for which a semi-analytical
expression is derived. Finally, even more general applications are discussed.
In all applications considered here it is found that
both the Newton and Faber integrators are fast, general, stable, and
accurate.
MSC: 65L05, 65E05, 81Q05