Ground-state electronic energies and densities of atomic systems in strong magnetic fields through a time-dependent hydrodynamical equation

Abstract

Through a single time-dependent (TD) quantum fluid dynamical equation of motion, ground-state electronic densities and energies in strong magnetic fields (up to 4.7 × 10¹¹ G) are calculated for H, H^-, He, Ne, and Ar atomic systems, by employing an imaginary-time evolution technique akin to quantum diffusion Monte Carlo method. The equation, based on TD density functional theory and quantum fluid dynamics, yields TD electron densities of a many-electron system in a real-time solution. It reduces to the TD Schrödinger equation for the H atom. For H^-, He, Ne, and Ar atoms, a local Wigner-type correlation functional is employed along with an improved local exchange functional. For Ne and Ar, a nonclassical correction term T_corr[ρ] is added to Weizscker's kinetic energy to obtain the correct kinetic energy and atomic shell structure. The results for the spin-free ground states are presented and compared with previous works wherever possible. At high fields, it is T_corr[ρ] that decides the actual state of the atom, instead of exchange and/or correlation functional, although the exchange effects dominate over the correlation effects.