RT Journal Article
T1 Stability of local quantum dissipative systems
A1 Cubitt, Toby S.
A1 Lucia, Angelo
A1 Michalakis, Spyridon
A1 Pérez García, David
AB 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.
PB Springer
SN 0010-3616
YR 2015
FD 2015-08-29
LK https://hdl.handle.net/20.500.14352/22975
UL https://hdl.handle.net/20.500.14352/22975
LA eng
NO Comunidad de Madrid
NO Ministerio de Ciencia e Innovación (MICINN)
NO Ministerio de Economía y Competitividad (MINECO)
NO European CHIST-ERA
NO Gordon and Betty Moore Foundation
NO AFOSR
DS Docta Complutense
RD 8 abr 2025