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The rigorous description of correlated quantum many-body systems constitutes one of the most challenging tasks in contemporary physics and related disciplines. In this context, a particularly useful tool is the concept of effective pair…
Static vortices close together are studied for two different models in 2-dimen- sional Euclidean space. In a simple model for one complex field an expansion in the parameters describing the relative position of two vortices can be given in…
Consider two capacitors in parallel, but initially isolated by a switch such that one is charged and the other not. After the switch is closed, the charges redistribute themselves in such a way that the final electrostatic energy is less…
We propose a set-up to realize two-channel Kondo physics using quantum dots. We discuss how the charge fluctuations on a small dot can be accessed by using a system of two single electron transistors arranged in parallel. We derive a…
We study the structure of Abrikosov vortices in two-band superconductors for different external magnetic fields and different parameters of the bands. The vortex core size determined by the coherence lengths are found to have qualitatively…
The superconducting proximity effect on two-dimensional massless Dirac electrons is usually analyzed using a simple model consisting of the Dirac Hamiltonian and an energy-independent pair potential. Although this conventional model is…
The capacitance of arbitrarily shaped objects is reformulated in terms of the Neumann-Poincar\'{e} operator. Capacitance is simply the dielectric permittivity of the surrounding medium multiplied by the area of the object and divided by the…
In this work we suggest very simple solution of the two capacitors paradox in the completely ideal (without any electrical resistance or inductive) electrical circuit. Namely, it is shown that electrical field energy loss corresponds to…
Assuming a logarithmic interaction between constituent particles, compact and locally accurate wave functions that describe bound states of the two-particle neutral and three-particle charged complexes in two dimensions are designed. Prime…
We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference…
An approximate analytical formula for the capacitance of a non-parallel plate capacitor with small values of inclination angles and distance separations of the plates is presented. Most applications involving position sensing that are…
The Casimir force between two metallic plates is affected by their roughness state. This effect is usually calculated through the so-called `proximity force approximation' which is only valid for small enough wavevectors in the spectrum of…
We proved that under quantum mechanics a momentum-energy and a space-time are dual vector spaces on an almost complex manifold in position representation, and the minimal uncertainty relations are equivalent to the inner-product relations…
Several new experiments have extended studies of the Casimir force into new and interesting regimes. This recent work will be briefly reviewed. With this recent progress, new issues with background electrostatic effects have been uncovered.…
We investigate the pseudo-Casimir force acting between two charged surfaces confining a single polyelectrolyte chain with opposite charge. We expand the exact free energy to the second order in the local electrostatic field as well as the…
We review the latest progress in understanding the fundamental noise properties of a coherent single electron emitter known as the mesoscopic capacitor. The system consists of a sub-micron cavity connected to a two-dimensional electron gas…
Interference of quasi bound states is studied in a ballistic electron ripple waveguide with two ripple cavities whose distance apart can be varied. This system is the waveguide analog of Dicke's model for two interacting atoms in a…
We study the Ginzburg-Landau equations in order to describe a two-dimensional superconductor in a bounded domain. Using the properties of a particular integrability point ($\kappa = 1/ \sqrt2$) of these nonlinear equations which allows…
We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that…
This document provides detailed descriptions of data acquisition and data analysis in support of the accompanying Article, cond-mat/0610721: Observation of the two-channel Kondo effect. Some of the most intriguing problems in solid state…