Related papers: Double-delta potentials: one dimensional scatterin…
We theoretically study the subband structure of single Si $\delta$-doped GaAs inserted in a quantum well and subject to an electric field applied along the growth direction. We use an efficient self-consistent procedure to solve…
This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…
The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. {\it Thermal fluctuations} of correlated fluids (such as critical…
The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex-energy solutions of the Schr\"odinger equation, typically when calculating their inner products. In quantum scattering theory the…
We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy…
We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet…
It is well-known that a delta potential well in 1D has only one bound state but that in 3D it supports an {\it infinite} number of bound states with {\it infinite} binding energy for the lowest level. We show how this also holds for the…
We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field $\varphi$ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong…
We construct a one-dimensional contact interaction ($\epsilon$ potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the $\epsilon$ potential and the Dirac's $\delta$ function,…
We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we…
We consider polarizable sheets, which recently received some attention, especially in context of the dispersion interaction of thin sheets like graphene. These sheets are modeled by a collection of delta function potentials and resemble…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…
The quantum vacuum effects are investigated for a massive scalar field with general curvature coupling and obeying the Robin boundary conditions given on two concentric spherical shells with radii $a $ and $b$ in the $D+1$-dimensional…
We consider quantum field theories with boundary on a codimension one hyperplane. Using 1+1 dimensional examples, we clarify the relation between three parameters characterising one-point functions, finite size corrections to the ground…
Quantities associated with Casimir forces are calculated in a model wave system of one spatial dimension with Dirichlet or Neumann boundary conditions. 1)Due to zero-point fluctuations, a partition is attracted to the walls of a box if the…
We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a…
We use a functional approach to evaluate the Casimir free energy for a self-interacting scalar field in $d+1$ dimensions, satisfying Dirichlet boundary conditions on two parallel planes. When the interaction is turned off, exact results for…
We review the analytic results for the phase shifts delta_{l}(k) in non-relativistic scattering from a spherical well. The conditions for the existence of resonances are established in terms of time-delays. Resonances are shown to exist for…
In the presence of an external field, the imposition of specific boundary conditions can lead to interesting new manifestations of the Casimir effect. In particular, it is shown here that even a single conducting plate may experience a…
Making use of the quantum correlators associated with the Maxwell field vacuum distorted by the presence of plane parallel material surfaces we derive the Casimir-Polder interaction in the presence of plane parallel conducting walls and in…