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Quantum spin chain dissipative mean-field dynamics

Benatti, F.; Carollo, Federico; Floreanini, R.; Narnhofer, H.

Authors

F. Benatti

Federico Carollo

R. Floreanini

H. Narnhofer



Abstract

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.

Journal Article Type Article
Publication Date Aug 10, 2018
Journal Journal of Physics A: Mathematical and Theoretical
Electronic ISSN 1751-8113
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 51
Issue 32
APA6 Citation Benatti, F., Carollo, F., Floreanini, R., & Narnhofer, H. (2018). Quantum spin chain dissipative mean-field dynamics. Journal of Physics A: Mathematical and Theoretical, 51(32), https://doi.org/10.1088/1751-8121/aacbdb
DOI https://doi.org/10.1088/1751-8121/aacbdb
Publisher URL http://iopscience.iop.org/article/10.1088/1751-8121/aacbdb/meta
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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