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Stability of local quantum dissipative systems

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Cubitt, Toby S. and Lucia, Angelo and Michalakis, Spyridon and Pérez García, David (2015) Stability of local quantum dissipative systems. Communications in Mathematical Physics, 337 (3). pp. 1275-1315. ISSN 0010-3616

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http://arxiv.org/abs/1303.4744v3Organisation


Abstract

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time which scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates which may not preserve detailed balance.


Item Type:Article
Uncontrolled Keywords:DETAILED BALANCE; THERMODYNAMICAL STABILITY; DYNAMICAL SEMIGROUPS; LATTICE SYSTEMS; KMS CONDITIONS; TRAPPED IONS; COMPUTATION; HYPERCONTRACTIVITY; SIMULATIONS; ANYONS
Subjects:Sciences > Physics > Quantum theory
ID Code:27982
Deposited On:13 Feb 2015 13:29
Last Modified:02 Jul 2015 11:16

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