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Stability of Local Quantum Dissipative Systems


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Authors

Cubitt, Toby S 
Lucia, Angelo 
Michalakis, Spyridon 
Perez-Garcia, David 

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.

Description

This is the author accepted manuscript. The final version is available from Springer at http://link.springer.com/article/10.1007%2Fs00220-015-2355-3.

Keywords

5108 Quantum Physics, 49 Mathematical Sciences, 51 Physical Sciences

Journal Title

Communications in Mathematical Physics

Conference Name

Journal ISSN

0010-3616
1432-0916

Volume Title

337

Publisher

Springer Science and Business Media LLC