State space distribution and dynamical flow for closed and open quantum systems
We present a general formalism for studying the effects of heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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AIP Publishing
2020
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| Online Access: | https://hdl.handle.net/1721.1/125411 |
| _version_ | 1811081411359145984 |
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| author | Dodin, Amro Willard, Adam P. |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Dodin, Amro Willard, Adam P. |
| author_sort | Dodin, Amro |
| collection | MIT |
| description | We present a general formalism for studying the effects of heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that is shown to be consistent with the derived analytical results. |
| first_indexed | 2024-09-23T11:46:15Z |
| format | Article |
| id | mit-1721.1/125411 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:46:15Z |
| publishDate | 2020 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1254112022-09-27T21:47:56Z State space distribution and dynamical flow for closed and open quantum systems Dodin, Amro Willard, Adam P. Massachusetts Institute of Technology. Department of Chemistry We present a general formalism for studying the effects of heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that is shown to be consistent with the derived analytical results. 2020-05-22T14:16:29Z 2020-05-22T14:16:29Z 2019-04 2020-01-14T15:28:45Z Article http://purl.org/eprint/type/JournalArticle 0021-9606 https://hdl.handle.net/1721.1/125411 Dodin, Amro and Adam P. Willard. “State space distribution and dynamical flow for closed and open quantum systems.” The Journal of chemical physics 15 (2019): 064106. en 10.1063/1.5100736 The Journal of chemical physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf AIP Publishing arXiv |
| spellingShingle | Dodin, Amro Willard, Adam P. State space distribution and dynamical flow for closed and open quantum systems |
| title | State space distribution and dynamical flow for closed and open quantum systems |
| title_full | State space distribution and dynamical flow for closed and open quantum systems |
| title_fullStr | State space distribution and dynamical flow for closed and open quantum systems |
| title_full_unstemmed | State space distribution and dynamical flow for closed and open quantum systems |
| title_short | State space distribution and dynamical flow for closed and open quantum systems |
| title_sort | state space distribution and dynamical flow for closed and open quantum systems |
| url | https://hdl.handle.net/1721.1/125411 |
| work_keys_str_mv | AT dodinamro statespacedistributionanddynamicalflowforclosedandopenquantumsystems AT willardadamp statespacedistributionanddynamicalflowforclosedandopenquantumsystems |