1302.6511 (Johannes Kern)

A perturbation theory for the Anderson model    [PDF]

Johannes Kern

Within the real-time approach, the current across a quantum dot which is tunnel coupled to two leads at different chemical potentials is calculated in two steps: One determines the reduced density matrix of the quantum dot by using the ``density matrix kernel'', and then the current by applying the ``current kernel'' to the reduced density matrix. If one multiplies the tunneling Hamiltonian by a coupling parameter ``w``, then everything, including the kernels and also the current, becomes a function of w. In the time space, the kernels have the clear structure of a power series in w, so one can speak about ''orders'' of the kernels. All odd orders and the constant terms vanish. Intuitively, one would guess that one can take the kernels of 2n-th order in order to obtain the current of 2n-th order, i.e., the coefficients of the Taylor expansion of the current in w=0 up to the order 2n. I want to show that this is true. I can address only the single impurity Anderson model (SIAM).

View original: http://arxiv.org/abs/1302.6511