title: Extended Vicsek fractals: Laplacian spectra and their applications.
abstract: Extended Vicsek fractals (EVF) are the structures constructed by introducing linear spacers into traditional Vicsek fractals. Here we study the Laplacian spectra of the EVF. In particularly, the recurrence relations for the Laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing Laplacian eigenvalues. This quantity characterizes the large-scale properties, such as the gyration radius of the polymeric structures, or the global mean-first passage time for the random walk processes. Introduction of the linear spacers leads to local heterogeneities, which reveal themselves, for example, in the dynamics of EVF under external forces.
authors.affiliation: Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany.|Institut Charles Sadron, Université de Strasbourg and CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
authors.forename: Maxim
authors.initials: M
authors.lastname: Dolgushev
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Hongxiao
authors.initials: H
authors.lastname: Liu
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Zhongzhi
authors.initials: Z
authors.lastname: Zhang