Related papers: An implicit split-operator algorithm for the nonlinear time-dependent Schr\"{o}dinger equation

An implicit split-operator algorithm for the nonlinear time-dependent Schr\"{o}dinger equation

URL: http://arxiv.org/abs/2109.10630v2
Date: Thu, 11 Nov 2021 10:21:56 GMT
Title: An implicit split-operator algorithm for the nonlinear time-dependent Schr\"{o}dinger equation
Authors: Julien Roulet, Ji\v{r}\'i Van\'i\v{c}ek
Abstract summary: The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr"odinger equations. We describe a family of high-order implicit splitoperator algorithms that are norm-conserving, time-reversible, and very efficient.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger 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.

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