Anomalous Diffusion on the Hanoi Networks

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dc.creatorBoettcher, S.
dc.creatorGoncalves, B.
dc.date2008-02-20
dc.date2008-09-15
dc.date.accessioned2026-07-07T10:09:43Z
dc.date.available2026-07-07T10:09:43Z
dc.descriptionDiffusion is modeled on the recently proposed Hanoi networks by studying the mean- square displacement of random walks with time, <r^2>~t^{2/d_w}. It is found that diffusion - the quintessential mode of transport throughout Nature - proceeds faster than ordinary, in one case with an exact, anomalous exponent dw = 2-log_2(ϕ) = 1.30576 . . .. It is an instance of a physical exponent containing the "golden ratio" ϕ=(1+\sqrt{5})/2 that is intimately related to Fibonacci sequences and since Euclid's time has been found to be fundamental throughout geometry, architecture, art, and Nature itself. It originates from a singular renormalization group fixed point with a subtle boundary layer, for whose resolution ϕis the main protagonist. The origin of this rare singularity is easily understood in terms of the physics of the process. Yet, the connection between network geometry and the emergence of ϕin this context remains elusive. These results provide an accurate test of recently proposed universal scaling forms for first passage times.
dc.description6 pages, 6 figures incl.; for related work, see http://www.physics.emory.edu/faculty/boettcher/, some new material, as to appear in Europhysics Letters
dc.identifierhttps://arxiv.org/abs/0802.2757
dc.identifierhttp://arxiv.org/abs/0802.2757
dc.identifierEuroPhysics Letters 84, 30002 (2008)
dc.identifierdoi:10.1209/0295-5075/84/30002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171409
dc.subjectStatistical Mechanics
dc.titleAnomalous Diffusion on the Hanoi Networks
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