Related papers: The Many-Electron System in the Forward, Exchange …
The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted…
Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix sigma-model. The method is based on replacing the initial model of interacting electons by a fully…
The problem of $N$ particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some quite remarkable specific cases have been solved in one dimension, whereas higher-dimensional exactly solved systems…
We report various many-body theoretical approaches to the nonlinear decay rate and energy loss of charged particles moving in an interacting free electron gas. These include perturbative formulations of the scattering matrix, the…
A one-dimensional cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a…
We develop a field theory formalism for the disordered interacting electron liquid in the dynamical Keldysh formulation. This formalism is an alternative to the previously used replica technique. In addition it naturally allows for the…
Many-body interactions in effective field theories for disordered interacting electrons are considered. It is shown that three-body and higher interaction terms are generated in perturbation theory, and some of the physical consequences of…
We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged…
We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole…
I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign…
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in…
We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the…
Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles.…
Quantum-electrodynamical density-functional theory (QEDFT) provides a promising avenue for exploring complex light-matter interactions in optical cavities for real materials. Similar to conventional density-functional theory, the Kohn-Sham…
The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals is available, but nearly all are based on the hierarchy of inputs commonly…
The emitted energy and the cross-section of classical scalar bremsstrahlung in massive particle collisions in D=4+d dimensional Minkowski space M_D as well as in the brane world M_4 \times T^d is computed to leading ultra-relativistic…
The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are…
Recently, no-go theorems for the existence of solitonic solutions in Einstein-Maxwell-scalar (EMS) models have been established in arXiv:1902.07721. Here we discuss how these theorems can be circumvented by a specific class of non-minimal…