Using the method developed in a recent paper (Euro. Phys. J. B 92.8 (2019): 1-28) we consider $1/f$ noise two-dimensional electron gas (2DEG). The coherence length of system is considered as basic parameter for discretizing space, inside which dynamics electrons described by quantum mechanics, while scales much larger than it semi-classical. For our model, based on Thomas-Fermi-Dirac approximat...