Related papers: Approximate normalizations for approximate density…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…
The assumption is made that only transversely polarized photons are needed for a correct description of Quantum Electrodynamics. A simple mathematical transformation is used to introduce new field operators which satisfy the full Maxwell…
A non-empirical exchange functional based on an interpolation between two limits of electron density: slowly varying limit and asymptotic limit, is proposed. In the slowly varying limit, we follow the study by Kleinman in 1984 which…
We calculate, as a function of temperature and density, the electron-electron interaction induced quasiparticle effective mass renormalization in 2D electron systems within the leading-order dynamically screened Coulomb interaction…
By analyzing the many-body problem for non-relativistic electrons strongly coupled to photon modes of a microcavity I derive the exact momentum/force balance equation for cavity quantum electrodynamics. Implications of this equation for the…
"Asymptotic formulae for likelihood-based tests of new physics" presents a mathematical formalism for a new approximation for hypothesis testing in high energy physics. The approximations are designed to greatly reduce the computational…
The exact interaction energy of a many-electron system is determined by the electron pair density, which is not well-approximated in standard Kohn-Sham density functional models. Here we study the (complicated but well-defined) exact…
Careful extrapolation of atomic correlation energies suggests that $E_c$ tends to $-AZ\log{Z} + BZ$ as $Z$ tends to infinity, where $Z$ is the atomic number, $A$ is known, and $B$ is about 38 milliHartrees. The coefficients roughly agree…
We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the…
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…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to…
The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the…
The statistics of energy levels of electrons in a random potential is considered in the critical energy window near the mobility edge. It is shown that the multifractality of critical wave functions results in the violation of the…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…
An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the…
Non-empty space reading of Maxwell equations as local energy identities explains why a Coulomb field is carried rigidly by electrons in experiments. The analytical solution of the Poisson equation defines the sharp radial shape of charged…
We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of [SS1,SS3]. Roughly speaking, it is obtained…
The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham…