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dc.contributor.authorSantos, Lea F.
dc.contributor.authorTorres-Herrera, E. Jonathan
dc.contributor.authorMéndez-Bermúdez, J. A.
dc.identifier.citationSantos, Lea F., E Jonathan Torres-Herrera, JA Méndez-Bermúdez. (2019). Level repulsion and dynamics in the finite one-dimensional Anderson model. Physical Review E 100(2): 022142en_US
dc.identifier.issnPrint: 1539-3755 Electronic: 1550-2376
dc.descriptionResearch article, peer-reviewed. Open Access.en_US
dc.description.abstractAbstract This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest-neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal on-site disorder strength W. But this is not the case when the model is finite and the localization length is larger than the system size L, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter ξ∝(W2L)−1. As ξ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster than when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for W=0, when it is in fact deeper.en_US
dc.description.sponsorshipACKNOWLEDGMENTS E.J.T.-H. and J.A.M.-B. acknowledge funding from VIEPBUAP (Grants No. MEBJ-EXC19-G, No. LUAG-EXC19-G, and No. CELU-EXC19-I), Mexico. They are also grateful to LNS-BUAP for allowing the use of the supercomputing facility. L.F.S. was supported by the NSF Grant No. DMR- 1603418.en_US
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofseriesPhysical Review E;100(2)
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.subjectSingle-particle dynamicsen_US
dc.subjectAnderson localizationen_US
dc.subjectRandom & disordered mediaen_US
dc.subjectCondensed Matter & Materials Physicsen_US
dc.subjectStatistical Physicsen_US
dc.titleLevel repulsion and dynamics in the finite one-dimensional Anderson model.en_US

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