Workshop book - Physikzentrum der RWTH Aachen - RWTH Aachen ...

Talks Monday February 4
The master equation for nanoscopic transport: Spectral analysis, perturbation
theory, and applications to molecular devices
Carsten Timm, Technische Universität Dresden, Germany
The master equation is a powerful method for the description of nanostructures
with strong interactions far from equilibrium. Using a master equation
for a molecular device coupled to a vibrational mode as an example, I will
analyze what information can be gained from the spectrum of eigenvalues
of the transition-rate matrix. So far, research has mostly focused on the
stationary state, which is the eigenstate to the (usually unique) vanishing
eigenvalue of this matrix. I will show that its full spectrum and its slowly
decaying eigenstates give useful information on the dynamics and are characteristic
of various regimes, such as the Coulomb and the Franck-Condon
blockade. In practice, the master equation is usually combined with perturbation
theory in the hybridization between the nanostructure and the electronic
leads. I will discuss recent theoretical progress regarding the exact time-convolutionless
(time-local) master equation to all orders in the hybridization.
Finally, I will comment on applications of the master equation to molecular
devices, including the direct comparison with break-junction experiments.
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