Related papers: Lower Bounds on the Exchange-Correlation Energy in…
Energy-energy correlators (EECs) provide a powerful tool to study the evolution of scattered partons into final-state hadrons. In these proceedings, a variety of energy correlator measurements performed by the ALICE collaboration are…
Binding energies calculated from using the Bethe-Salpeter equation in the simplest ladder approximation significantly differ from those obtained in the non-relativistic standard instantaneous approximation. While they should a priori be…
The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…
We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\"odinger perturbation theory to show that, in…
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations…
We briefly review the physics of electronic phases in low dimensional conductors. We begin by introducing the properties of the one-dimensional electron gas model using bosonization and renormalization group methods.We then tackle the…
We present a systematic study of bound relations between different electronic properties of magnetic crystals: electron density, effective mass, orbital magnetization, localization length, Chern invariant, and electric susceptibility. All…
Energy correlators are field-theoretically clean and phenomenologically valuable probes of QCD dynamics. We explore the possibility of using the information encoded in the energy correlators of a hadronically decaying electroweak vector…
A novel formulation of the electron energy relaxation terms is presented here, which is applicable to plasma flows and discharges wherein the electron temperature could be higher or lower than the gas temperature. It is demonstrated that…
The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with…
A new method to determine electron correlation energy is described. This method is based on a better representation of the potential due to interacting electrons that is obtained by specifying both the average and standard deviation. The…
A functional $E_{xc}[\rho(\r,\epsilon)]$ is presented, in which the exchange and correlation energy of an electron gas depends on the local density of occupied states. A simple local parametrization scheme is proposed, entirely from first…
We consider the conductance of a one-dimensional wire interrupted by a double-barrier structure allowing for a resonant level. Using the electron-electron interaction strength as a small parameter, we are able to build a non-perturbative…
The computational treatment of many-electron systems capable of exchanging {electrons and nuclei} with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of…
Motivated by the considerable importance of material properties in modern condensed matter physics research, and using techniques of the $N_{e}$ -electron systems in terms of the electron density $n_{\sigma e}\left( r\right) $ needed to…
We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…
We study the critical behaviour near the threshold where a first bound state appears at some value of coupling constant in an attractive short-range potential in $2+\epsilon $ dimensions. We obtain general expression for the binding energy…
The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description…
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in…