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Spectral properties of simple classical and quantum reset processes

dc.contributor.authorRose, Dominic C.en_ZA
dc.contributor.authorTouchette, Hugoen_ZA
dc.contributor.authorLesanovsky, Igoren_ZA
dc.contributor.authorGarrahan, Juan P.en_ZA
dc.date.accessioned2019-10-25T10:19:56Z
dc.date.available2019-10-25T10:19:56Z
dc.date.issued2018
dc.identifier.citationRose, D. C., et al. 2018. Spectral properties of simple classical and quantum reset processes. Physical Review E, 98(2):022129, doi:10.1103/PhysRevE.98.022129en_ZA
dc.identifier.issn2470-0053 (online)
dc.identifier.issn2470-0045 (print)
dc.identifier.otherdoi:10.1103/PhysRevE.98.022129
dc.identifier.urihttp://hdl.handle.net/10019.1/106728
dc.descriptionCITATION: Rose, D. C., et al. 2018. Spectral properties of simple classical and quantum reset processes. Physical Review E, 98(2):022129, doi:10.1103/PhysRevE.98.022129.en_ZA
dc.descriptionThe original publication is available at https://journals.aps.org/preen_ZA
dc.description.abstractWe study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that this simple reset dynamics causes a uniform shift in the eigenvalues of the Markov generator, excluding the zero mode corresponding to the stationary state, which has the effect of accelerating or even inducing relaxation to a stationary state. Based on this result, we provide expressions for the stationary state and probability current of the reset process in terms of weighted sums over dynamical modes of the reset-free process. We also discuss the effect of resets on processes that display metastability. We illustrate our results with two classical stochastic processes, the totally asymmetric random walk and the one-dimensional Brownian motion, as well as two quantum models: a particle coherently hopping on a chain and the dissipative transverse field Ising model, known to exhibit metastability.en_ZA
dc.description.urihttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.022129
dc.format.extent10 pages : colour illustrationsen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherAmerican Physical Societyen_ZA
dc.subjectSpectral propertiesen_ZA
dc.subjectBrownian motionen_ZA
dc.subjectQuantum systemsen_ZA
dc.subjectMetastability (Physics)en_ZA
dc.subjectStochastic processen_ZA
dc.titleSpectral properties of simple classical and quantum reset processesen_ZA
dc.typeArticleen_ZA
dc.description.versionPublisher's versionen_ZA
dc.rights.holderAmerican Physical Societyen_ZA


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