  Without access to the full quantum state, modeling dissipation in an open
system requires approximations. The physical soundness of such approximations
relies on using realistic microscopic models of dissipation that satisfy
completely positive dynamical maps. Here we present an approach based on the
use of the Bohmian conditional wave function that, by construction, ensures a
completely positive dynamical map for either Markovian or non-Markovian
scenarios, while allowing the implementation of realistic dissipation sources.
Our approach is applied to compute the current-voltage characteristic of a
resonant tunneling device with a parabolic-band structure, including
electron-lattice interactions. A stochastic Schr\"odinger equation is solved
for the conditional wave function of each simulated electron. We also extend
our approach to (graphene-like) materials with a linear band-structure using
Bohmian conditional spinors for a stochastic Dirac equation.
