Computation of quantum electrical currents through the ramo-shockley- pellegrini theorem with trajectories

Motivated by a recent approach to solve quantum dynamics with full Coulomb correlations [X. Oriols, Phys. Rev. Lett. 98 (2007) 066803], we present here an extension of the Ramo-Shockley-Pellegrini theorem for quantum systems to compute the total (conduction plus displacement) current in terms of quantum (Bohmian) trajectories. By way of test, we derive an extension of the Ramo-Shockley- Pellegrini theorem using standard quantum mechanics and we compare it to our former result. As expected, both formulations give identical results, however we emphasize the numerical viability of computing self-consistently the total current by means of quantum trajectories in front of the difficulties to do it in terms of standard quantum mechanics. © 2012 World Scientific Publishing Company.