LAUSR

Recently the Luttinger field approach was proposed by Eich et al. in Phys. Rev B 90, 115116 (2014) as a way to simulate switching on a temperature gradient across a nanoscale device initially in thermal equilibrium. The time dependent particle and heat currents can then be calculated by propagating the initial equilibrium state of the system in time. Unfortunately applying a uniform Luttinger field in the whole of a lead causes a discrepancy between steady state currents in the long time limit and those predicted by the Landauer-Büttiker formulas as well as artefacts at short times. Here we propose a modified approach where the Luttinger field gradually reaches its final value across a transition region. If the length of the transition region is sufficient, the electrons move through without reflecting. In this way the correct energy distribution of electrons originating from such a lead, corresponding to the new temperature, is established in the scattering region. Our approach is tested on a single quantum dot and a parallel double quantum dot system.