25.05.2007 11 c.t.
The classical limit of quantum transport
by Prof. Dr. Piet Brouwer
from Cornell University, Ithaca, USA
Seminarraum Haus 2, 4. Stock (Bunsenstr.)
The interference of multiply scattered quantum mechanical matter waves is the origin of small but noticeable corrections to the electrical conductance of a metal at low temperatures. Being an interference phenomenon, this correction is statistical in nature, highly dependent on the precise location of impurities in the metal. Historically, one separates the interference correction to the electrical conductance into `weak localization', a small negative correction to the conductance averaged over an ensemble of conductors with different impurity configurations, and the `conductance fluctuations', the sample-to-sample fluctuations measured with respect to the ensemble average. What is the fate of quantum interference corrections in the limit that the wavelength of the electrons becomes small in comparison to all other relevant length scales of the device? This limit is a `classical limit' similar to the transition from wave optics to ray optics that occurs once the typical size of optical elements becomes much larger than the wavelength of light. In electronic transport, this situation is realized in semiconductor `quantum dots', small metallic islands in which the electron motion is ballistic and the only source of scattering is reflection off smooth sample boundaries. In this talk I'll show that, whereas the interference correction to the ensemble-averaged conductance (weak localization) disappears in this limit, the quantum interference contribution to the sample-specific conductance fluctuations remains surprisingly unaffected.
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