A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arise...
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| Format: | Article |
| Language: | en_US |
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American Institute of Physics (AIP)
2015
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| Online Access: | http://hdl.handle.net/1721.1/94525 https://orcid.org/0000-0001-7616-7809 |
| _version_ | 1826212365570408448 |
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| author | Moix, Jeremy Cao, Jianshu |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Moix, Jeremy Cao, Jianshu |
| author_sort | Moix, Jeremy |
| collection | MIT |
| description | The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Forster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes. |
| first_indexed | 2024-09-23T15:20:33Z |
| format | Article |
| id | mit-1721.1/94525 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:20:33Z |
| publishDate | 2015 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/945252022-10-02T02:18:41Z A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems Moix, Jeremy Cao, Jianshu Massachusetts Institute of Technology. Department of Chemistry Moix, Jeremy Cao, Jianshu The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Forster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes. National Science Foundation (U.S.) (Grant CHE-1112825) United States. Defense Advanced Research Projects Agency (Grant N99001-10-1-4063) United States. Dept. of Energy. Office of Basic Energy Sciences (Award DE-SC0001088) 2015-02-13T16:16:05Z 2015-02-13T16:16:05Z 2013-10 2013-08 Article http://purl.org/eprint/type/JournalArticle 00219606 1089-7690 http://hdl.handle.net/1721.1/94525 Moix, Jeremy M., and Jianshu Cao. “A Hybrid Stochastic Hierarchy Equations of Motion Approach to Treat the Low Temperature Dynamics of Non-Markovian Open Quantum Systems.” The Journal of Chemical Physics 139, no. 13 (2013): 134106. © 2013 AIP Publishing LLC https://orcid.org/0000-0001-7616-7809 en_US http://dx.doi.org/10.1063/1.4822043 The Journal of Chemical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics (AIP) MIT web domain |
| spellingShingle | Moix, Jeremy Cao, Jianshu A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems |
| title | A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems |
| title_full | A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems |
| title_fullStr | A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems |
| title_full_unstemmed | A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems |
| title_short | A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems |
| title_sort | hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non markovian open quantum systems |
| url | http://hdl.handle.net/1721.1/94525 https://orcid.org/0000-0001-7616-7809 |
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