A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations
We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In t...
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American Institute of Physics (AIP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/113235 https://orcid.org/0000-0002-3931-001X https://orcid.org/0000-0001-7616-7809 |
| _version_ | 1826214341283676160 |
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| author | Hsieh, Chang Yu Cao, Jianshu |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Hsieh, Chang Yu Cao, Jianshu |
| author_sort | Hsieh, Chang Yu |
| collection | MIT |
| description | We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism. |
| first_indexed | 2024-09-23T16:03:30Z |
| format | Article |
| id | mit-1721.1/113235 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:03:30Z |
| publishDate | 2018 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/1132352022-10-02T06:03:38Z A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations Hsieh, Chang Yu Cao, Jianshu Massachusetts Institute of Technology. Department of Chemistry Hsieh, Chang Yu Cao, Jianshu We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism. National Science Foundation (U.S.) (Grant CHE-1112825) Singapore-MIT Alliance for Research and Technology (SMART) 2018-01-19T15:53:03Z 2018-01-19T15:53:03Z 2018-01 2017 2018-01-17T17:15:47Z Article http://purl.org/eprint/type/JournalArticle 0021-9606 1089-7690 http://hdl.handle.net/1721.1/113235 Hsieh, Chang-Yu, and Jianshu Cao. “A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations.” The Journal of Chemical Physics, vol. 148, no. 1, Jan. 2018, p. 014103. https://orcid.org/0000-0002-3931-001X https://orcid.org/0000-0001-7616-7809 http://dx.doi.org/10.1063/1.5018725 The Journal of Chemical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf American Institute of Physics (AIP) arXiv |
| spellingShingle | Hsieh, Chang Yu Cao, Jianshu A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations |
| title | A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations |
| title_full | A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations |
| title_fullStr | A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations |
| title_full_unstemmed | A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations |
| title_short | A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations |
| title_sort | unified stochastic formulation of dissipative quantum dynamics i generalized hierarchical equations |
| url | http://hdl.handle.net/1721.1/113235 https://orcid.org/0000-0002-3931-001X https://orcid.org/0000-0001-7616-7809 |
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