相关论文: Relativistic Strong Scott Conjecture: A Short Proo…
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy,…
Outer crusts of neutron stars and interiors of cool white dwarfs consist of bare atomic nuclei, arranged in a crystal lattice and immersed in a Fermi gas of degenerate electrons. We study electrostatic properties of such Coulomb crystals,…
When a Hamiltonian density is bounded by below, we know that the lowest-energy state must be stable. One is often tempted to reverse the theorem and therefore believe that an unbounded Hamiltonian density always implies an instability. The…
We present the results of numerical calculations of magnetizability ($\chi$) of the relativistic one-electron atoms with a pointlike, spinless and motionless nuclei of charge $Ze$. Exploiting the analytical formula for $\chi$ recently…
This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to infinity with the magnetic field B satisfying B >> Z^{4/3} all the electrons…
In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De…
Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the…
Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago. For…
We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and…
We are at a specific period of modern cosmology, during which the large increase of the amount of data leads to the idea that the determination of cosmological parameters has been achieved with a rather good precision. There is a large…
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…
The lightest supersymmetric particle (LSP) is stable in an R-parity conserving theory. In this article the steps needed to calculate the present day mass density of such a particle are detailed. It is shown that there can be a…
Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are…
In this work we show that relativistic contributions to the ground state energy of the hydrogen atom arising from the presence of a minimal length introduced by a Lorentz-covariant algebra are more relevant than non-relativistic ones, and…
We calculate the ground state properties of recently synthesized superheavy nuclei starting from $Z$=105-120. The nonrelativistic and relativistic mean field formalisms is used to evaluate the binding energy, charge radius, quadrupole…
The static properties of some possible light and moderate kaonic nuclei, from C to Ti, are studied in the relativistic mean-field theory. The 1s and 1p state binding energies of $K^-$ are in the range of $73\sim 96$ MeV and $22\sim 63$ MeV,…
We provide a proof of the first correction to the leading asymptotics of the minimal energy of pseudo-relativistic molecules in the presence of magnetic fields, the so-called "relativistic Scott correction", when $\max{Z_k\alpha} \leq…
We give a review of experimental and theoretical results on the precision study of hydrogen-like atoms with low value of the nuclear charge Z.
Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact…
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schr\"odinger perturbation theory, with the use of the Sturmian series expansion of the generalized…