Quantum spin chain dissipative mean-field dynamics

Benatti, F. and Carollo, F. and 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

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Physics and Astronomy
Identification Number: https://doi.org/10.1088/1751-8121/aacbdb
Depositing User: Eprints, Support
Date Deposited: 26 Jul 2018 08:50
Last Modified: 29 Jun 2019 04:30
URI: http://eprints.nottingham.ac.uk/id/eprint/53157

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