Zobrazeno 1 - 10
of 161
pro vyhledávání: '"Siedentop, Heinz"'
Autor:
Meng, Long, Siedentop, Heinz
We study atomic ground state energies for neutral atoms as the nuclear charge $Z$ is large in the no-pair formalism. We show that for a large class of projections defining the underlying Dirac sea -- covering not only the physical reasonable cases bu
Externí odkaz:
http://arxiv.org/abs/2411.07046
We collect estimates of the exchange energy of the relativistic no-pair Hartree-Fock and M\"uller functional and use them to show the existence of a minimizer and stability of matter of the relativistic M\"uller functional in the free picture.
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Externí odkaz:
http://arxiv.org/abs/2408.17158
Publikováno v:
Letters in Mathematical Physics, Volume 113 (2023), no. 1, Paper No. 11
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the limit of a
Externí odkaz:
http://arxiv.org/abs/2204.10081
Autor:
Siedentop, Heinz
We review some of the basic mathematical results about density functional theory.
Externí odkaz:
http://arxiv.org/abs/2203.14069
Autor:
Siedentop, Heinz
We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation of the lowe
Externí odkaz:
http://arxiv.org/abs/2101.06539
The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizs\"acker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.
Externí odkaz:
http://arxiv.org/abs/2010.12074
Publikováno v:
Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 41 (2023), 69-79
We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic energy $(c^2p^2+c^4)^{1/2}-c^2$ used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the limit $Z,c\to\
Externí odkaz:
http://arxiv.org/abs/2009.02474
Autor:
Merz, Konstantin, Siedentop, Heinz
Publikováno v:
Annales Henri Lebesgue, Volume 5 (2022), pp. 611-642
We prove the convergence of the density on the scale $Z^{-1}$ to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known to describe heavy atoms accurately.
Externí odkaz:
http://arxiv.org/abs/2007.03895
Autor:
Chen, Hongshuo, Siedentop, Heinz
Publikováno v:
Journal of Physics A: Mathematical and Theoretical, 53, 395201 (2020)
We show that the molecular relativistic Thomas-Fermi-Weizs\"acker 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+
Externí odkaz:
http://arxiv.org/abs/1912.00205
Publikováno v:
Pure Appl. Funct. Anal. 5, 1319-1356 (2020)
We consider a large neutral atom of atomic number $Z$, taking relativistic effects into account by assuming the dispersion relation $\sqrt{c^2p^2+c^4}$. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in th
Externí odkaz:
http://arxiv.org/abs/1907.04894