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A new repeated-slab calculation method is developed to simulate the electronic structures of charged surfaces by arranging density-variable charged sheets in vacuum regions to realize a constant potential on the charged sheets and maintain…
We study the force between two circular electrodes in different configurations. A formula analogous to Kelvin's formula for the spheres is given in the case of equal disks held at the same potential and when one plate is earthed. An…
When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The…
The tunability of binding energies is explored by modulating a finite dielectric slab width in a planar, three dielectric system. After verifying the equivalence of the field method and method of images, three different configurations are…
Within the Poisson-Boltzmann (PB) approach electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance $C$ on the surface charge density $\sigma$ and the ionic…
We study the exchange coupling in small Wigner crystals confined to one-dimensional space. In particular we concentrate on the simplest nontrivial case of two electrons in a box potential and calculate analytically the energy splitting…
We study the classic problem of the capacitance of a circular parallel plate capacitor. At small separations between the plates, it is initially considered in 19th century by Kirchhoff who found the leading and the subleading term in the…
Cubature formulas, asymptotically optimal with respect to accuracy, are derived for calculating multidimensional weakly singular integrals. They are used for developing a universal code for calculating capacitances of conductors of…
The distribution of electric fields within the electrochemical double layer depends on both the electrode and electrolyte in complex ways. These fields strongly influence chemical dynamics in the electrode-electrolyte interface, but cannot…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the…
Coaxial 2-terminal bridge comparison is a widely used metrological method in the dissemination of value of capacitance up to 1000 pF and $10^4$ rad/s. In this range, capacitance can be measured with uncertainties as small as few parts in…
This tutorial paper shows how to compute the DC (or low-frequency) resistance, inductance and capacitance of a pair of parallel wires using the finite element method. A three-dimensional infinite domain (open boundary) modeling of…
We discuss the possibility that the electron may be fractionalized in some quantum phases of matter in two or higher dimensions. We review the theory of such phases, and show that their effective theory is a $Z_2$ gauge theory. These phases…
Electronic states in nanographite ribbons with zigzag edges are studied using the extended Hubbard model with nearest neighbor Coulomb interactions. The electronic states with the opposite electric charges separated along both edges are…
A method is given for estimating clamped plane elastica. Arguments are made, and evidence is provided by way of illustrative examples, suggesting that the new method is quicker and more robust than standard discretisation, and more likely…
The capacitance of the electric double layer has potential applications in supercapacitors, and theoretical investigations of the double-layer capacitance in binary mixtures are important. In this work, we develop the theory of the electric…
We study a class of exactly solvable models for strongly correlated electrons, defined on a set of N cells, and with infinite on-site repulsion on part of the sites of each cell. For 2N or more electrons the exact ground state is known. We…
Minimum total energy calculations, which account for both electron--lattice and electron--electron interactions in conjugated polymers are performed for chains with up to eight carbon atoms. These calculations are motivated in part by…
The potential energy of a static charge distribution on a lattice is rigorously computed in the standard compact quantum electrodynamic model. The method used follows closely that of Weyl for ordinary quantum electrodynamics in continuous…