Thomas-Fermi-von Weizsacker 理论中二维材料的均匀化

Convergence Rates from Yukawa to Coulomb Interaction in the Thomas-Fermi-von Weizsäcker Model

We establish uniform convergence, with explicit rate, of the solution to the Thomas--Fermi--von Weizsäcker (TFW) Yukawa model to the solution of the TFW Coulomb model, for general condensed nuclear configurations. As a consequence, we show the convergence of forces from the Yukawa to the Coulomb model. These results rely on an extension of Nazar \& Ortner (2015) to the Yukawa setting. Auxiliary results of independent interest shown also include new existence, uniqueness and stability results for the Yukawa ground state.

Locality of the Thomas-Fermi-von Weizsäcker Equations

We establish a pointwise stability estimate for the Thomas-Fermi-von Weizsäcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy int…

Cauchy-Born rule and spin density wave for the spin-polarized Thomas-Fermi-Dirac-von Weizsacker model

The electronic structure (electron charges and spins) of a perfect crystal under external magnetic field is analyzed using the spin-polarized Thomas-Fermi-Dirac-von Weizsacker model. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions on charge density wave and spin density wave. A Landau-Lifschitz type micromagnetic energy functional is derived.

The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory

We prove that in Thomas-Fermi-Dirac-von Weizsäcker theory, a nucleus of charge $Z>0$ can bind at most $Z+C$ electrons, where $C$ is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.

Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker theory with small nuclear charges

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.

广义Thomas-Fermi-Weizsäcker泛函的过剩电荷界

Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals

该研究针对广义Thomas-Fermi-Weizsäcker密度泛函，界定原子过剩电子数，证明3/2<p<2时过剩电荷在原子序数中一致有界，明确p=3/2为临界情形并改进p≥6/5时的线性界。