Dresden 2009 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 2: Transport: Nanoelectronics I - Quantum Dots and Wires, Point Contacts 1

TT 2.9: Talk

Monday, March 23, 2009, 12:30–12:45, HSZ 301

Tunneling through nanostructures: random matrix theory for the rate equation — •Carsten Timm — Institut für Theoretische Physik, Technische Universität Dresden

Under the conditions of weak hybridization and rapid dephasing, electronic tunneling through quantum dots or single molecules can be described by rate equations. Except for highly simplified models, one typically finds rather complex structures in the differential conductance. Random matrix theory has been used to describe statistical properties of the energy spectrum in such cases. Here, we follow a different approach: The rate equations for the probabilities P_n of states of the nanosystem can be written as dP_m/dt = ∑_n A_mn P_n. The eigenvalues of the stochastic matrix A describe the relaxational and oscillatory dynamics of the probabilities. We take A to be a random matrix. We discuss ensembles realized by these matrices and present results for the distribution and correlations of their eigenvalues.