TY - JOUR
T1 - High order three part split symplectic integrators
T2 - Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation
AU - Skokos, Ch
AU - Gerlach, E.
AU - Bodyfelt, J. D.
AU - Papamikos, G.
AU - Eggl, S.
N1 - Funding Information:
We thank the anonymous referee for many valuable suggestions that helped us to greatly improve our paper. Ch.S. would like to thank S. Anastasiou, G. Benettin and J. Laskar for useful discussions, as well as the Max Planck Institute for the Physics of Complex Systems in Dresden for its hospitality during his visits in 2012 and 2013, when part of this work was carried out. Ch.S. was supported by the Research Committee, Aristotle University of Thessaloniki (Prog. No. 89317 ) and the University of Cape Town (Start-Up Grant, Fund No. 459221 ), as well as by the European Union ( European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: “THALES. Investing in knowledge society through the European Social Fund”. S.E. acknowledges the support of the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement No. 282703 . E.G. would like to thank P. Jung for fruitful discussions.
PY - 2014/5/16
Y1 - 2014/5/16
N2 - While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS - a hotly debated subject in current scientific literature.
AB - While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS - a hotly debated subject in current scientific literature.
KW - Disorder
KW - Multidimensional Hamiltonian systems
KW - Nonlinear Schrödinger equation
KW - Symplectic integrators
KW - Three part split
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U2 - 10.1016/j.physleta.2014.04.050
DO - 10.1016/j.physleta.2014.04.050
M3 - Article
AN - SCOPUS:84901617081
SN - 0375-9601
VL - 378
SP - 1809
EP - 1815
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 26-27
ER -