This study investigates the influence of material density, disorder in onsite energies, and localization length on relaxation dynamics within a two-dimensional random site Coulomb glass model at half-filling. To explore relaxation laws, we calculate the eigenvalue distribution of the linear dynamical matrix using mean-field approximations. Our findings indicate that the system initially undergoes rapid relaxation through energy-lowering transitions. The depletion of the single-particle density of states (DOS) near the Fermi level leads to slow relaxation, with fluctuations diminishing according to a power law. Subsequently, the system adheres to an exponential decay law after a specific period, defined as the relaxation time, which is inversely related to the minimum eigenvalue of the dynamical matrix. As the density of the system decreases, the relaxation rate slows down, resulting in an increase in the relaxation time. For a constant density and localization length, an increase in the disorder of onsite energies results in a longer relaxation time. A significant portion of the eigenvalue spectrum remains unaffected, suggesting that a reduction in localization length concurrent with increased disorder may play an equally vital role in the slow dynamics observed.

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• Nonequilibrium statistical mechanics
• Disordered systems
• Master equation