TY - JOUR

T1 - Random-matrix modeling of semilinear response, the generalized variable-range hopping picture, and the conductance of mesoscopic rings

AU - Stotland, Alexander

AU - Kottos, Tsampikos

AU - Cohen, Doron

PY - 2010/3/31

Y1 - 2010/3/31

N2 - Semilinear response theory determines the absorption coefficient of a driven system using a resistor network calculation: each unperturbed energy level of a particle in a vibrating trap, or of an electron in a mesoscopic ring, is regarded as a node (n) of the network; the transition rates (wmn) between the nodes are regarded as the elements of a random matrix that describes the network. If the size distribution of the connecting elements is wide (e.g., log-normal-like rather than Gaussian type) the result for the absorption coefficient differs enormously from the conventional Kubo prediction of linear response theory. We use a generalized variable range hopping scheme for the analysis. In particular, we apply this approach to obtain practical approximations for the conductance of mesoscopic rings. In this context Mott's picture of diffusion and localization is revisited.

AB - Semilinear response theory determines the absorption coefficient of a driven system using a resistor network calculation: each unperturbed energy level of a particle in a vibrating trap, or of an electron in a mesoscopic ring, is regarded as a node (n) of the network; the transition rates (wmn) between the nodes are regarded as the elements of a random matrix that describes the network. If the size distribution of the connecting elements is wide (e.g., log-normal-like rather than Gaussian type) the result for the absorption coefficient differs enormously from the conventional Kubo prediction of linear response theory. We use a generalized variable range hopping scheme for the analysis. In particular, we apply this approach to obtain practical approximations for the conductance of mesoscopic rings. In this context Mott's picture of diffusion and localization is revisited.

UR - http://www.scopus.com/inward/record.url?scp=77955070497&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.81.115464

DO - 10.1103/PhysRevB.81.115464

M3 - Article

AN - SCOPUS:77955070497

SN - 1098-0121

VL - 81

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 11

M1 - 115464

ER -