Convergence of the TFDW Energy to the Liquid Drop Model
Published in SIAM Journal of Mathematical Analysis, 2021
Recommended citation: L. Aguirre Salazar, S. Alama, and L. Bronsard (2021). " Convergence of the TFDW Energy to the Liquid Drop Model " SIAM J. Math. Anal. 53(3) pp. 3493-3519. https://doi.org/10.1137/20M1344329
We consider two nonlocal variational models arising in physical contexts. The first is the Thomas-Fermi-Dirac-von Weizsacker (TFDW) model, introduced in the study of ionization of atoms and molecules, and the second is the liquid drop model with external potential, proposed by Gamow in the context of nuclear structure. It has been observed that the two models exhibit many of the same properties, especially in regard to the existence and nonexistence of minimizers. We show that, under a “sharp interface” scaling of the coefficients, the TFDW energy with constrained mass Γ-converges to the liquid drop model for a general class of external potentials. Finally, we present some consequences for global minimization of each model.
Recommended citation: L. Aguirre Salazar, S. Alama, and L. Bronsard (2021). " Convergence of the TFDW Energy to the Liquid Drop Model " SIAM J. Math. Anal. 53(3) pp. 3493-3519.