  This study presents a Monte Carlo simulation tool for modeling the
transportation processes of thermal electrons in noble liquids, specifically
focusing on liquid argon and liquid xenon. The study aims to elucidate the
microscopical mechanisms governing the drift and diffusion of electrons within
the context of time projection chambers (TPCs), with detailed considerations of
coherent electron-atom scattering and electric field force. The simulation tool
is implemented in the Geant4 framework, allowing for the exploration of
electron transport parameters, including drift velocity, longitudinal diffusion
coefficient, and transverse diffusion coefficient. The simulation is validated
by comparing its results for drift velocity and diffusion coefficients with
experimental measurements, revealing good agreement in the low to moderate
electric field ranges. Discrepancies in high electric field regions are
discussed, highlighting the impact of impurities and the need for improved
cross-section calculations. Despite some limitations, the simulation tool
provides valuable insights into electron transport in noble liquids, offering a
foundation for future enhancements and applications in diverse research areas.
