Paper Info
Title
A Bloch Decomposition-Based Split-Step Pseudospectral Method for Quantum Dynamics with Periodic Potentials
Abstract
We present a new numerical method for accurate computations of solutions to (linear) one-dimensional Schro¨dinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by nonperiodic potentials describing external electric fields. Our approach is based on the classical Bloch decomposition method, which allows us to diagonalize the periodic part of the Hamiltonian operator. Hence, the dominant effects from dispersion and periodic lattice potential are computed together, while the nonperiodic potential acts only as a perturbation. Because the split-step communicator error between the periodic and nonperiodic parts is relatively small, the step size can be chosen substantially larger than for the traditional splitting of the dispersion and potential operators. Indeed it is shown by the given examples that our method is unconditionally stable and more efficient than the traditional split-step pseudospectral schemes. To this end a particular focus is on the semiclassical regime, where the new algorithm naturally incorporates the adiabatic splitting of slow and fast degrees of freedom.
Year
DOI
Venue
2007
10.1137/060652026
SIAM J. Scientific Computing
Keywords
DocType
Volume
nonperiodic potential,adiabatic splitting,potential operator,nonperiodic part,Periodic Potentials,lattice potential,time-splitting spectral method,new numerical method,new algorithm,schrodinger equation,Bloch Decomposition-Based Split-Step Pseudospectral,classical Bloch decomposition method,semi- classical asymptotics,Quantum Dynamics,periodic part,periodic potential,periodic lattice potential,bloch decomposition
Journal
29
Issue
ISSN
Citations 
2
1064-8275
8
PageRank 
References 
Authors
0.77
2
4
Name
Order
Citations
PageRank
Zhongyi Huang16712.67
Shi Jin257285.54
Peter A. Markowich36413.62
Christof Sparber4327.35