Stochastic Schrödinger equations and conditional states: A general non-Markovian quantum electron transport simulator for THz electronics

Abstract

A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantumsystems bymeans of state vectors haswell known computational advantages. In this respect, the physicalmeaning of the so-called conditional states inMarkovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schrodinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction (linked to the corresponding Bohmian trajectory) as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees offreedom. As an example of the practical utility of these states, we present a time-dependent quantumMonte Carlo algorithmto describe electron transport in open quantum systems under general (Markovian or non-Markovian) conditions. By making the most of trajectory-based and wavefunction methods, the resulting simulation technique extends to the quantum regime, the computational capabilities that theMonte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.