Consideration of electronic mean heat transport via a low dimension system

The object of research is the complex realm of energy localization and coherent ballistic electronic transport within low-dimensional silicon quantum wires, specifically those doped with germanium atoms. Unlike their three-dimensional counterparts, low-dimensional systems exhibit unique electronic transport behaviors, necessitating novel analytical approaches for a comprehensive understanding. The core of this investigation leverages the Phase Field Matching Theory (PMFT) and the tight-binding (TB) approximation, sophisticated methodologies that enable a deep dive into the quantum mechanical nuances of these systems. Through this lens, we examine the intricate dynamics of dispersion relationships, phase factors, group velocities, and notably, the impact of defects introduced by the germanium doping.This research meticulously analyzes how these defects affect electronic and thermal conductivities, along with densities of states, offering new insights into the role of Fano resonances in the fluctuation of transmission and reflection spectra. These resonances, we find, are crucially dependent on the nature of the defects, their configuration, and the electronic parameters in their vicinity, underscoring the nuanced interplay between material composition and electronic properties in low-dimensional systems.The implications of our findings extend far beyond the theoretical. They pave the way for significant advancements in nanotechnology and the design of electronic devices, highlighting the potential for creating more efficient, high-performance components. Furthermore, this work proposes a framework for developing non-destructive testing methodologies that could revolutionize material science by enabling the precise analysis of defects in low-dimensional systems without causing damage. This is particularly critical for the ongoing development of materials with optimized properties for various applications, from electronics to energy storage.In essence, this research not only enriches our understanding of the physics governing low-dimensional systems but also offers practical insights into leveraging these properties for technological innovation. By bridging the gap between theoretical physics and material science, our study sets the stage for the next generation of electronic components and non-destructive evaluation techniques, marking a significant step forward in the application of quantum mechanics to real-world challenges.