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The majority of experimental realizations of single-electron sources rely on the periodic manipulation of the tunnel junctions through their gate voltages, and thus require a high level of control over the system. To circumvent the…
In the literature on electron-phonon scatterings very often a phenomenological expression for the transition matrix element is used which was derived in the textbooks of Ashcroft/Mermin and of Czycholl. There are various steps in the…
A simple systematic method for calculating derivative expansions of the one-loop effective action is presented. This method is based on using symbols of operators and well known deformation quantization theory. To demonstrate its advantages…
An analytical expression for the current through a single level quantum dot for arbitrary strength of the on-site electron-electron interaction is derived beyond standard mean-field theory. By describing the localised states in terms of…
A time operator $\hat T_\eps$ of the one-dimensional harmonic oscillator $ \hat h_\eps=\half(p^2+\eps q^2)$ is rigorously constructed. It is formally expressed as $ \hat T_\eps=\half\frac{1}{\sqrt \eps } (\arctan (\sqrt \eps \hat…
We use the Foldy--Wouthuysen (unitary) transformation to give an alternative characterization of the eigenvalues and eigenfunctions for the Brown-Ravenhall operator (the projected Dirac operator) in the case of a one-electron atom. In…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…
In this article we present a novel semi-analytical approach to calculate first-order electron-vibration coupling constants within the framework of density functional theory. It combines analytical expressions for the first-order derivative…
An alternative multipole expansion of the correlation term is derived. Modified spherical Bessel type functions which simplify as a summation of multiple orders of basic trigonometric functions are generated from this new method. We use…
A system of electrons in a local or nonlocal external potential can be studied with 1-matrix functional theory (1MFT), which is similar to density functional theory (DFT) but takes the one-particle reduced density matrix (1-matrix) instead…
We develop a general algebraic scheme to decompose fractional quantum Hall (FQH) wave functions based on the operator contraction multiplication. By introducing fermionic and bosonic operators and establishing three fundamental contraction…
Using the coherent state formalism we calculate matrix elements of the one-loop non-planar dilatation operator of ${\cal N}=4$ SYM between operators dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior. We comment…
The account of electron correlation and its efficient separation into dynamic and nondynamic parts plays a key role in the development of computational methods. In this paper we suggest a physically-sound matrix formulation to split…
We present a calculation of the electromagnetic form factors of the $\rho^+$ meson. Our formalism is based on the point-form of relativistic quantum mechanics. Electron-$\rho$-meson scattering is formulated as a coupled-channel problem for…
In a recent paper, Klaseboer et al. (IEEE Trans. Antennas Propag., vol. 65, no. 2, pp. 972-977, Feb. 2017) developed a surface integral formulation of electromagnetics that does not require working with integral equations that have singular…
The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
A boundary integral formulation of electromagnetics that involves only the components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use of surface currents that appear in the classical PMCHWT formulation. The kernels of…
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…
We briefly review and illustrate our procedure to 'decouple' by transformation of generators: either a Hopf algebra $H$ from a $H$-module algebra $A_1$ in their cross-product $A_1 >\triangleleft H$; or two (or more) $H$-module algebras…