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	A Bloch decomposition-based split-step pseudospectral method for quantum dynamics with periodic potentials
	Huang, Zhongyi ; Jin, Shi ; Markowich, Peter A. ; Sparber, Christof
	2010-05-06 ; 2010-05-06
关键词	Schrodinger equation Bloch decomposition time-splitting spectral method semi-classical asymptotics lattice potential MULTIPHASE SEMICLASSICAL APPROXIMATION DIMENSIONAL CRYSTALLINE LATTICE MONTE-CARLO ANALYSIS BAND-STRUCTURE SEMICONDUCTOR-DEVICES SCHRODINGER-EQUATION ELECTRON HOMOGENIZATION Mathematics, Applied
中文摘要	We present a new numerical method for accurate computations of solutions to ( linear) one-dimensional Schrodinger 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.
语种	英语 ; 英语
出版者	SIAM PUBLICATIONS ; PHILADELPHIA ; 3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14304]
专题	清华大学
推荐引用方式 GB/T 7714	Huang, Zhongyi,Jin, Shi,Markowich, Peter A.,et al. A Bloch decomposition-based split-step pseudospectral method for quantum dynamics with periodic potentials[J],2010, 2010.
APA	Huang, Zhongyi,Jin, Shi,Markowich, Peter A.,&Sparber, Christof.(2010).A Bloch decomposition-based split-step pseudospectral method for quantum dynamics with periodic potentials..
MLA	Huang, Zhongyi,et al."A Bloch decomposition-based split-step pseudospectral method for quantum dynamics with periodic potentials".(2010).

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