arXiv subjects

Hongshuo Chen

Publications and source records attributed to Hongshuo Chen.

3 recordsLinked to original sources

arXiv2023

Derivation of Vlasov equations for multi-species fermions

We explore a system of two-species fermions with $N$ particles. Through this exploration, we establish a two-species Husimi measure and construct a two-species Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy with error terms. We provide proofs of the smallness of these errors in the semiclassical and mean-field limits, fixing $\hbar = N^{-1/3}$. After that, we rigorously establish the uniqueness of this hierarchy. This allows us to conclude that the two-species Husimi measure from the solution of the $N$-particle Schr\"odinger equation approximates the solution of the Vlasov equation for two-species systems.

math-ph↗

arXiv2020

A Statistical Theory of Heavy Atoms: Energy and Excess Charge

The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizsäcker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.

math-ph↗

arXiv2020

On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction

We show that the molecular relativistic Thomas-Fermi-Weizsäcker functional consisting of atoms of atomic numbers $Z_1,...,Z_k$ has a minimizer, if the particle number $N$ is constrained to a number less or equal to the total nuclear charge $Z:=Z_1+...+Z_K$. Moreover, there is no minimizer, if the particle number exceeds $2.56 Z$. This gives lower and upper bounds on the maximal ionization of heavy atoms.

math-ph↗