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Rapid mixing and stability of quantum dissipative systems

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Lucia, Angelo 
Cubitt, Toby S 
Michalakis, Spyridon 
Pérez-García, David 


The physics of many materials is modeled by quantum many-body systems with local interactions. If the model of the system is sensitive to noise from the environment, or small perturbations to the original interactions, it will not model properly the robustness of the real physical system it aims to describe, or be useful when engineering novel systems for quantum information processing. We show that local observables and correlation functions of local Liouvillians are stable to local perturbations if the dynamics is rapidly mixing and has a unique xed point. No other condition is required.


This is the author accepted manuscript. The final version is available from APS at


5108 Quantum Physics, 51 Physical Sciences

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Physical Review A

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American Physical Society (APS)
T. S. C. is supported by the Royal Society, and was pre- viously supported by the Juan de la Cierva program of the Spanish MICIM. A. L. and D. P.-G. acknowledge support from MINECO (grant MTM2011-26912), Comunidad de Madrid (grant QUITEMAD+-CM, ref. S2013/ICE-2801) and the European CHIST-ERA project CQC (funded partially by MINECO grant PRI-PIMCHI-2011-1071). A. L. is supported by MINECO FPI fellowship BES-2012- 052404. S. M. acknowledges funding provided by IQIM, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant #GBMF1250, and AFOSR Grant #FA8750-12-2-0308. The authors would like to thank the hospitality of the Centro de Ciencias Pedro Pascual in Benasque, where part of this work was carried out.