Stochastic Schr\"{o}dinger equations and conditional states: a general Non-Markovian quantum electron transport simulator for THz electronics

TL;DR

This paper introduces a quantum Monte Carlo method using conditional wavefunctions to simulate electron transport in open quantum systems, effectively handling both Markovian and non-Markovian dynamics, and extending classical transport simulation capabilities.

Contribution

It proposes a novel stochastic Schrödinger equation framework based on Bohmian conditional wavefunctions for non-Markovian quantum transport simulation.

Findings

Developed a time-dependent quantum Monte Carlo algorithm for electron transport.

Extended classical Monte Carlo methods to the quantum regime.

Demonstrated applicability to general open quantum systems.

Abstract

A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schr\"{o}dinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of freedom. As an example of the practical utility of these states, we present a time-dependent quantum Monte Carlo algorithm to 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 the Monte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.