Exact e–e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensive N = 3 , 4 , … , ′ n ′ -electron systems via multi-pole expansion

Inclusion of coulomb interaction emerges with the complexity of either convergence of integrals or separation of variables of Schrödinger equations. For an N-electron system, interaction terms grow by N(N-1)/2 factors. Therefore, 2-e system stands as fundamental basic unit for generalized N-e systems. For the first time, we have evaluated e–e correlations in very simple and absolutely terminating finite summed hypergeometric series for 2-D double carrier parabolic quantum dot in both zero and arbitrary non-zero magnetic field (symmetric gauge) and have appraised these integrals in variational methods. The competitive role among confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium on energy level diagram, level-spacing statistics, heat capacities (C_v at 1 K) and magnetization ($T\sim$(0–1)K) is studied on systems spanning over wide range of materials (GaAs,Ge,CdS,SiO₂ and He, etc). We have also constructed an exact theory for generalized correlated N-e 2-D quantum dots via multi-pole expansion but for the sake of compactness of the article we refrain from data.