Abstract
Transport phenomena are fundamental to understanding and optimizing quantum systems. This study investigates the transport properties of multidot quantum systems configured in series and parallel combinations, emphasizing two key aspects: the Wiedemann-Franz (WF) law and the Thermodynamic Uncertainty Relation (TUR). Using the scattering approach within the linear response framework, we analyze transmission functions, thermoelectric properties, and TUR. A general expression for quantum corrections under constant transmission conditions, where electron tunneling is probabilistic, is derived. Our findings reveal critical insights: (i) quantum phase transitions between weak and strong coupling regimes in parallel configurations, (ii) consistent violations of the WF law across all systems, and (iii) adherence to the TUR in the presence of the Aharonov-Bohm (AB) phase. Additionally, we report distinctive behaviors in transmission and thermoelectric properties, including charge and thermal conductance, the Lorenz ratio, and thermopower. For both constant and phase-dependent transmission scenarios, the TUR value consistently satisfies ≥ thresholds, and quantum corrections remain positive, underscoring their robustness. These results advance the understanding of quantum transport and provide a framework for optimizing performance in multidot quantum systems.