چكيده لاتين
Anderson localization, a phenomenon where wave interference in disordered systems prevents the propagation of particles, has been a cornerstone in understanding transport properties in condensed matter physics. While extensively studied in Hermitian systems, recent advancements in non-Hermitian quantum mechanics have opened new avenues for exploring localization phenomena under conditions where energy conservation and other traditional constraints no longer apply. This thesis investigates non-Hermitian Anderson localization, merging the realms of disordered systems and non-Hermitian physics to uncover novel physical phenomena and potential applications. We start our analysis first by providing an in-depth introduction to Anderson localization, beginning with the fundamental principles of quantum transport in disordered media and extending to its theoretical framework and experimental realizations. The interplay between disorder, interference, and dimensionality is analyzed in detail, alongside discussions on the scaling theory and applications in real-world systems. Then, the focus shifts to non-Hermitian systems, where we explore the mathematical foundations, historical developments, and motivations for studying these unconventional frameworks. Non-Hermitian operators, characterized by complex eigenvalues, introduce novel features such as exceptional points, non-Hermitian skin effects, and unique topological behaviors, reshaping traditional quantum mechanics. Theoretical models and experimental platforms relevant to non-Hermitian systems are critically reviewed. Finally,we delves into the intersection of these fields, presenting a comprehensive study of Anderson localization in non-Hermitian systems. Using both analytical and numerical approaches, we explores how non-Hermiticity modifies localization phenomena, introducing complex eigenvalue spectra, gain-loss dynamics, and novel scaling laws. The role of exceptional points in driving localization-delocalization transitions is highlighted, revealing unique signatures that distinguish non-Hermitian Anderson localization from its Hermitian counterpart.
