On the symplectic integration of the discrete nonlinear Schr\'odinger equation with disorder

Autor:	Gerlach, Enrico, Meichsner, Jan, Skokos, Charalampos
Rok vydání:	2015
Předmět:	Physics - Computational Physics Condensed Matter - Disordered Systems and Neural Networks Condensed Matter - Statistical Mechanics Mathematical Physics Nonlinear Sciences - Chaotic Dynamics
Druh dokumentu:	Working Paper
Popis:	We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS) equation, and compare their efficiency. Our results suggest that the most suitable methods for the very long time integration of this one-dimensional Hamiltonian lattice model with many degrees of freedom (of the order of a few hundreds) are the ones based on three part splits of the system's Hamiltonian. Two part split techniques can be preferred for relatively small lattices having up to $N\approx\;$70 sites. An advantage of the latter methods is the better conservation of the system's second integral, i.e. the wave packet's norm. Comment: 12 pages, 3 figures, accepted for publication in EPJ ST
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.07778 Zobrazit plný text záznamu View this record from Arxiv