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Faber and Newton Polynomial Integrators for Open-System Density Matrix Propagation
Please always quote using this URN: urn:nbn:de:0297-zib-3725
- 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.
Author: | Wilhelm Huisinga, Lorenzo Pesce, Ronnie Kosloff, Peter Saalfrank |
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Document Type: | ZIB-Report |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Exx Numerical methods in complex analysis (potential theory, etc.) (For numerical methods in conformal mapping, see also 30C30) / 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical methods in conformal mapping, see *also* 30C30 |
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems | |
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein- Gordon and other equations of quantum mechanics | |
Date of first Publication: | 1998/11/03 |
Series (Serial Number): | ZIB-Report (SC-98-29) |
ZIB-Reportnumber: | SC-98-29 |
Published in: | Appeared in: J. Chem. Phys. 110 (1999) 12 |