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

TL;DR

This paper introduces a Bohmian conditional wave function approach for modeling quantum dissipation in open systems, ensuring physically consistent dynamics and enabling realistic simulations of nanoscale electron devices with complex band structures.

Contribution

It presents a novel method using Bohmian conditional wave functions to model dissipation with guaranteed complete positivity, applicable to both Markovian and non-Markovian regimes.

Findings

Successfully simulated current-voltage characteristics of a resonant tunneling device.

Extended the method to graphene-like materials with linear band structures.

Demonstrated the approach's ability to incorporate electron-lattice interactions.

Abstract

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.