Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 18: Brownian motion and transport II

DY 18.2: Vortrag

Dienstag, 27. März 2007, 17:00–17:15, H3

Electrical resistance of disordered one-dimensional quantum conductors — •Christophe Deroulers — Institut für Theoretische Physik, Köln, Deutschland

In some (quasi-)one-dimensional quantum conductors (nanowires, anisotropic crystals, ...), it is observed that the electrical resistance R behaves, in some temperature range, as a power of the temperature T. Some results do not coincide with the well-known predictions of Kane and Fisher for a Luttinger liquid with a few weak impurities, and we study if these results could be due to disorder (many strong impurities in the wire). In our model, the wire is randomly cut in a chain of weakly-coupled “quantum dots” between which electrons hop. Because of competition betweenn tunneling and activation, and because of some interesting statistical effects, R behaves at low temperatures like exp(1/√T) and, at higher temperatures, like a complicated function that may look like a power-law over one or two decades, as in experiments. We show, based on numerical simulations, that these two regimes are also distinguished by the repartition of current in the network of resistances equivalent to one wire, and that the statistical distribution of lnR is non-trivial and is given, for some temperatures, by an extreme value statistics (Gumbel law).