Fingerprints of classical diffusion in open 2D . . .

We investigate the distribution of theresonanc widths and Wigner delay times ) for scfi3q[+(8 from two-dimensional systems in the di#usive regime. We obtain the forms of these distributions (log-normal for large #W and small #, and power law in the opposite cite for di#erent symmetryc lasses and show that they are determined by the underlying di#usive cfi+q#[(8 dynamic( Our theoretic2 arguments are supported by extensive numeric+ cic+(8#2#RR Quantum scattering has been a subject of intensive research activity both in mesoscopic physics and in Quantum Chaos in the le3 years [1--7]. Among the most interesting quantities for the description of a scattering process are the Wignerdel y times and resonance widths. The former quantity captures the time-dependent aspects of quantum scattering. It can be interpreted as the typical time anal[W] monochromatic wave packet remains in the interaction region. It is relCjW to the energy derivative of thetotal phase shift #(E)= -i det S(E) of the scattering matrix S(E), i.e. # W (E)= d#(E) dE . Resonances are defined as polk of the S-matrix occurring atcomplW energies E n = E n # n , where E n is the position and # n the width of the resonance. They correspond to "eigenstates" of the open system that decay in time due to the couplAto the "outside worlkFor chaotic/balqC3l systems Random Matrix Theory (RMT) is appl]W3Q[w and the distributions of resonance widths Wignerdel y times ) are known [2]. As the disorder increases, the system becomes di#usive and the deviations from RMT become increasingl apparent. In thestrongl disorderedliso wherel ocalACCW3Q dominates, the distribution of resonances [4] and del y times ) [5] were found recentl . At the same time, an attempt to understand systems atcritical condition..

Measuring preferential attachment in evolving networks

A key ingredient of ma y current models proposed tocaT00= the topologica evolution of complex networks is the hypothesis tha highly connected nodes increa4 their connectivityfa)#F tha their less connected peers,a phenomenon caFN# preferentia a tta hment