Quantum spin chain dissipative mean-field dynamics
We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the commutative algebra of mean-field operators, the quasi-local algeb...
| Main Authors: | , , , |
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| Format: | Article |
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IOP Publishing
2018
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| Online Access: | https://eprints.nottingham.ac.uk/53157/ |
| _version_ | 1848798889654616064 |
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| author | Benatti, F. Carollo, F. Floreanini, R. Narnhofer, H. |
| author_facet | Benatti, F. Carollo, F. Floreanini, R. Narnhofer, H. |
| author_sort | Benatti, F. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the commutative algebra of mean-field operators, the quasi-local algebra of microscopic, local operators and the collective algebra of fluctuation operators. In the infinite volume limit, mean-field operators behave as time-dependent, commuting scalar macroscopic averages while quasi-local operators, despite the dissipative underlying dynamics, evolve unitarily in a typical non-Markovian fashion. Instead, the algebra of collective fluctuations, which is of bosonic type with time-dependent canonical commutation relations, undergoes a time-evolution that retains the dissipative character of the underlying microscopic dynamics and exhibits non-linear features. These latter disappear by extending the time-evolution to a larger algebra where it is represented by a continuous one-parameter semigroup of completely positive maps. The corresponding generator is not of Lindblad form and displays mixed quantum-classical features, thus indicating that peculiar hybrid systems may naturally emerge at the level of quantum fluctuations in many-body quantum systems endowed with non time-invariant states. |
| first_indexed | 2025-11-14T20:26:57Z |
| format | Article |
| id | nottingham-53157 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:26:57Z |
| publishDate | 2018 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-531572020-05-04T19:48:22Z https://eprints.nottingham.ac.uk/53157/ Quantum spin chain dissipative mean-field dynamics Benatti, F. Carollo, F. Floreanini, R. Narnhofer, H. We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the commutative algebra of mean-field operators, the quasi-local algebra of microscopic, local operators and the collective algebra of fluctuation operators. In the infinite volume limit, mean-field operators behave as time-dependent, commuting scalar macroscopic averages while quasi-local operators, despite the dissipative underlying dynamics, evolve unitarily in a typical non-Markovian fashion. Instead, the algebra of collective fluctuations, which is of bosonic type with time-dependent canonical commutation relations, undergoes a time-evolution that retains the dissipative character of the underlying microscopic dynamics and exhibits non-linear features. These latter disappear by extending the time-evolution to a larger algebra where it is represented by a continuous one-parameter semigroup of completely positive maps. The corresponding generator is not of Lindblad form and displays mixed quantum-classical features, thus indicating that peculiar hybrid systems may naturally emerge at the level of quantum fluctuations in many-body quantum systems endowed with non time-invariant states. IOP Publishing 2018-08-10 Article PeerReviewed Benatti, F., Carollo, F., Floreanini, R. and Narnhofer, H. (2018) Quantum spin chain dissipative mean-field dynamics. Journal of Physics A: Mathematical and Theoretical, 51 (32). p. 325001. ISSN 1751-8113 http://iopscience.iop.org/article/10.1088/1751-8121/aacbdb/meta doi:10.1088/1751-8121/aacbdb doi:10.1088/1751-8121/aacbdb |
| spellingShingle | Benatti, F. Carollo, F. Floreanini, R. Narnhofer, H. Quantum spin chain dissipative mean-field dynamics |
| title | Quantum spin chain dissipative mean-field dynamics |
| title_full | Quantum spin chain dissipative mean-field dynamics |
| title_fullStr | Quantum spin chain dissipative mean-field dynamics |
| title_full_unstemmed | Quantum spin chain dissipative mean-field dynamics |
| title_short | Quantum spin chain dissipative mean-field dynamics |
| title_sort | quantum spin chain dissipative mean-field dynamics |
| url | https://eprints.nottingham.ac.uk/53157/ https://eprints.nottingham.ac.uk/53157/ https://eprints.nottingham.ac.uk/53157/ |