OFFPRINTQuantum chaotic scattering in graphenesystemsR. Yang, L. Huang, Y.-C. Lai and C. GrebogiEPL, 94 (2011) 40004Please visit the new websitewww.epljournal.orgThe Editorial Board invites you to submit your letters to EPLSix good reasons to publish with EPLWe want to work with you to help gain recognition for your high-quality work through worldwide visibility and high citations. 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Ván 2010 EPL 89 30001; artistic impression by Frédérique Swist).May 2011EPL, 94 (2011) 40004 www.epljournal.orgdoi: 10.1209/0295-5075/94/40004Quantum chaotic scattering in graphene systemsRui Yang1, Liang Huang1,2, Ying-Cheng Lai1,3,4and Celso Grebogi41School of Electrical, Computer and Energy Engineering, Arizona State University - Tempe, AZ 85287, USA2Institute of Computational Physics and Complex Systems, and Key Laboratory for Magnetism and MagneticMaterials of MOE, Lanzhou University - Lanzhou, Gansu 730000, China3Department of Physics, Arizona State University - Tempe, AZ 85287, USA4Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences,King’s College, University of Aberdeen - Aberdeen, UK, EUreceived 5 December 2010; accepted in final form 8 April 2011published online 11 May 2011PAC S 05.45.Mt – Quantum chaos; semiclassical methodsPAC S 72.80.Vp – Electronic transport in graphenePAC S 73.23.-b – Electronic transport in mesoscopic systemsAbstract – We investigate the transport fluctuations in both non-relativistic quantum dots andgraphene quantum dots with both hyperbolic and nonhyperbolic chaotic scattering dynamics inthe classical limit. We find that nonhyperbolic dots generate sharper resonances than those in thehyperboli c case. Strikingly, for the graphene dots, the resonances t end to be much sharper. Thismeans that transmission or conductance fluctuations are characteristically greatly enhanced inrelativistic as compared to non-relativistic quantum systems.Copyrightc EPLA, 2011In the last three decades, quantum chaos, an interdis-ciplinary field focusing on the quantum manifestations ofclassical chaos, has received a great deal of attention [1].In fact, the quantization of chaotic Hamiltonian systemsand the ensuing quantum signatures of classical chaosare fundamental procedure and process, respectively, inphysics, having direct applications in condensed matterphysics, atomic physics, nuclear physics, optics, andacoustics. However, most existing works on quantumchaos are concerned with non-relativistic quantum-mechanical systems described by the Schr¨odingerequation. Since the quasi-particles of graphene are chiral,massless Dirac fermions [2,3], the fundamental issue ofrelativistic quantum manifestations of chaos in graphenesystems has attracted a great deal of recent attention.Topics that have b een studied include level-spacingstatistics, transition from regular to chaotic dynam-ics, relativistic quantum scars, and weak localization,etc. [4,5]. In this letter, we study the fu nd amentalproblem of relativistic quantum scattering using graphenechaotic billiards and compare the results with those fromnon-relativistic quantum-dot systems.In open Hamiltonian systems, there are two kindsof