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Without access to the full quantum state, modeling dissipation in an opensystem requires approximations. The physical soundness of such approximationsrelies on using realistic microscopic models of dissipation that satisfycompletely positive dynamical maps. Here we present an approach based on theuse of the Bohmian conditional wave function that, by construction, ensures acompletely positive dynamical map for either Markovian or non-Markovianscenarios, while allowing the implementation of realistic dissipation sources.Our approach is applied to compute the current-voltage characteristic of aresonant tunneling device with a parabolic-band structure, includingelectron-lattice interactions. A stochastic Schr\"odinger equation is solvedfor the conditional wave function of each simulated electron. We also extendour approach to (graphene-like) materials with a linear band-structure usingBohmian conditional spinors for a stochastic Dirac equation.

Quantum dissipation with conditional wave functions: Application to the realistic simulation of nanoscale electron devices