Quantum spin chain dissipative mean-field dynamics

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

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.

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

• Journal Article Type: Article
• Acceptance Date: Jun 12, 2018
• Online Publication Date: Jun 29, 2018
• Publication Date: Aug 10, 2018
• Deposit Date: Jul 26, 2018
• Publicly Available Date: Jun 30, 2019
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 32
• DOI: https://doi.org/10.1088/1751-8121/aacbdb
• Public URL: https://nottingham-repository.worktribe.com/output/948934
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8121/aacbdb/meta
• Contract Date: Jul 26, 2018