3.6.1 Elecron-Electron Interaction

The self-consistent HARTREE self-energy due to electron-electron interaction is given by [205]

 \Sigma_\mathrm{el-el}({\bf r_1},t_1) \
...e = \ -\ensuremath {\mathrm{q}}\phi({\bf r_1}) \ .
 \end{array}\end{displaymath} (3.46)

where $ \varrho({\bf r},t)/(-\ensuremath {\mathrm{q}}) =n({\bf r},t)=-i\hbar G({\bf r},t,{\bf r},t)$ (see Section 3.9.1). The potential $ \phi$ resulting from the HARTREE self-energy is in fact the solution of the POISSON equation with the charge density $ \varrho$. The HARTREE self-energy is instantaneous. M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors