Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential
The computation of the Schrödinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require inexpensive but accurate solutions over large spatio-temporal window...
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2018
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| _version_ | 1826301102390247424 |
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| author | Iserles, A Kropielnicka, K Singh, P |
| author_facet | Iserles, A Kropielnicka, K Singh, P |
| author_sort | Iserles, A |
| collection | OXFORD |
| description | The computation of the Schrödinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require inexpensive but accurate solutions over large spatio-temporal windows. In this work we develop Magnus expansions where commutators have been simplified. Consequently, the exponentiation of these Magnus expansions via Lanczos iterations is significantly cheaper than that for traditional Magnus expansions. At the same time, and unlike most competing methods, we simplify integrals instead of discretizing them via quadrature at the outset—this gives us the flexibility to handle a variety of potentials, being particularly effective in the case of highly oscillatory potentials, where this strategy allows us to consider significantly larger time steps. |
| first_indexed | 2024-03-07T05:27:18Z |
| format | Journal article |
| id | oxford-uuid:e100ad67-c0fb-4eeb-b9c4-596ce7e02fc2 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:27:18Z |
| publishDate | 2018 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:e100ad67-c0fb-4eeb-b9c4-596ce7e02fc22022-03-27T09:51:18ZMagnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potentialJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e100ad67-c0fb-4eeb-b9c4-596ce7e02fc2Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2018Iserles, AKropielnicka, KSingh, PThe computation of the Schrödinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require inexpensive but accurate solutions over large spatio-temporal windows. In this work we develop Magnus expansions where commutators have been simplified. Consequently, the exponentiation of these Magnus expansions via Lanczos iterations is significantly cheaper than that for traditional Magnus expansions. At the same time, and unlike most competing methods, we simplify integrals instead of discretizing them via quadrature at the outset—this gives us the flexibility to handle a variety of potentials, being particularly effective in the case of highly oscillatory potentials, where this strategy allows us to consider significantly larger time steps. |
| spellingShingle | Iserles, A Kropielnicka, K Singh, P Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential |
| title | Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential |
| title_full | Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential |
| title_fullStr | Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential |
| title_full_unstemmed | Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential |
| title_short | Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential |
| title_sort | magnus lanczos methods with simplified commutators for the schrodinger equation with a time dependent potential |
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