1302.1391 (Johannes Kern)

Tunneling Hamiltonian    [PDF]

Johannes Kern

I work on the description of the transport of electrons across a quantum dot which is tunnel coupled to leads at different chemical potentials. A Hamilton operator which rules the time evolution of the system containing the leads and the quantum dot is needed for this. As it is usual, I assume that the total Hamiltonian is the sum of three contributions: That of the leads (noninteracting electrons), that of the quantum dot and a third one, the "tunneling Hamiltonian" which reflects the possibility that electrons can move from the leads to the quantum dot or vice versa. I will ask the question why the Hamiltonian of the composite system should have this form. I will start the discussion with the total Hamiltonian of the system acting on a many-electron wave function, including the attractive interaction between nuclei and electrons as well as the repulsive Coulomb-interaction between different electrons. Indeed, a natural separation of the total Hamiltonian in the described form will be obtained. An analysis of the tunneling Hamiltonian shows that the electron-electron interaction yields contributions to it which represent the correlated tunneling of two electrons at the same time.

View original: http://arxiv.org/abs/1302.1391