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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Accesso online: | https://arxiv.org/abs/2109.10630 |
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| _version_ | 1866929513784410112 |
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| author | Roulet, Julien Vaníček, Jiří |
| author_facet | Roulet, Julien Vaníček, Jiří |
| contents | The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrödinger equations. However, when applied to certain nonlinear time-dependent Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10630 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation Roulet, Julien Vaníček, Jiří Chemical Physics Computational Physics Quantum Physics The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrödinger equations. However, when applied to certain nonlinear time-dependent Schrödinger 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. |
| title | An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation |
| topic | Chemical Physics Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2109.10630 |