Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

TL;DR

This paper explores modeling quantum scattering in open systems using Bohmian conditional wave functions, emphasizing transitions between single-particle states with well-defined energies, applicable to light-matter interactions.

Contribution

It introduces a framework using BCWF to model scattering with non-commuting energy and momentum operators, applicable to non-Markovian quantum transport scenarios.

Findings

BCWF allows rigorous analysis of electron dynamics in open quantum systems.

The method models light-matter interactions in resonant tunneling devices.

Scattering is interpreted as transitions between energy-defined single-particle states.

Abstract

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by the non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWF) allow a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of such single-particle pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light-matter interaction phenomena in a resonant tunneling device (RTD), where a single photon is interacting with a single electron. Third, we emphasize the importance of interpreting such scattering mechanism as a transition between initial and final single-particle BCWF with well-defined energies (rather than with well-defined momenta).