Quantum master equation for electron transport through quantum dots and single molecules
Abstract
A quantum master equation (QME) is derived for the manybody density matrix of an open currentcarrying system weaklycoupled to two metal leads. The dynamics and the steadystate properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of the number of electrons in the system. We show that coherences between system states with different number of electrons, n (Fock space coherences), do not contribute to the transport to second order in systemlead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order of or faster than the system Bohr frequencies. For large bias, when all the system manybody states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation (when the damping is slow compared to the Bohr frequencies), the dynamics of populations and coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.
 Publication:

Physical Review B
 Pub Date:
 December 2006
 DOI:
 10.1103/PhysRevB.74.235309
 arXiv:
 arXiv:condmat/0610004
 Bibcode:
 2006PhRvB..74w5309H
 Keywords:

 73.63.b;
 03.65.Yz;
 05.60.Gg;
 Electronic transport in nanoscale materials and structures;
 Decoherence;
 open systems;
 quantum statistical methods;
 Quantum transport;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 22 pages, 8 figures, paper accepted in Phys. Rev. B