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An implicit split-operator algorithm for the nonlinear time-dependent Schrodinger equation
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DOI：10.1063/5.0071153.png)
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The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrodinger equations. However, when applied to certain nonlinear time-dependent Schrodinger equations, this algorithm loses time reversibility and second-order accuracy, which makes it very inefficient. Here, we propose to overcome the limitations of the explicit split-operator algorithm by abandoning its explicit nature. We describe a family of high-order implicit split-operator algorithms that are norm-conserving, time-reversible, and very efficient. The geometric properties of the integrators are proven analytically and demonstrated numerically on the local control of a two-dimensional model of retinal. Although they are only applicable to separable Hamiltonians, the implicit split-operator algorithms are, in this setting, more efficient than the recently proposed integrators based on the implicit midpoint method.& nbsp;(C)2021 Author(s).
Keyword:
BOSE-EINSTEIN CONDENSATION
GROSS-PITAEVSKII EQUATION
FOURIER METHOD SOLUTION
WAVE-PACKET DYNAMICS
QUANTUM DYNAMICS
LOCAL-CONTROL
COMPOSITION CONSTANTS
SCHEMES
VORTEX
期刊
IF:
3.1
论文数:
7.2W
被引数:
23.2W
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