Related papers: On summation of Kapteyn series
This note is concerned with series of the forms $\sum f(a^n)$ and $\sum f(n^{-a})$ where f(a) possesses a Mellin transform and $a > 1$ or $a<0$ respectively. Integral representations are derived and used to transform these series in several…
In our Comment we question the validity of the claim made by the authors of \cite{cc} that their solutions of the Dirac equation in an external {\em time-dependent} electromagnetic field describe beams of electrons. In every time-dependent…
Spatially indirect excitons in semiconducting double quantum wells have been shown to exhibit rich collective many-body behavior that result from the nature of the extended dipole-dipole interactions between particles. For many…
We explore excitation transport within a one-dimensional chain of atoms where the atomic transition dipoles are coupled to the free radiation field. When the atoms are separated by distances smaller or comparable to the wavelength of the…
Along the development of free-electron laser operating at the wavelength of X-ray, the importance of investigation on the radiation has increased. A theoretical simulation is an essential tool for studying existing and proposed experiments.…
Using our recently developed equivalent circuit model of radiative heat transfer we analyze the far-field thermal emission from bodies of constrained dimensions. We prove that the power radiated by a hypothetical metamaterial emitter which…
We investigate the spatially and temporally resolved electron kinetics in a homogeneous electric field in argon gas, in the vicinity of an emitting boundary. This (transient) region, where the electron swarm exhibits non-equilibrium…
We develop a manifest non-Hermitian approach of spectral and transport properties of two- dimensional mesoscopic systems in strong magnetic field. The finite system to which several ter- minals are attached constitutes an open system that…
We consider special Lambert series as generating functions of divisor sums and determine their complete transseries expansion near rational roots of unity. Our methods also yield new insights into the Laurent expansions and modularity…
Ultrafast light-matter interaction is a powerful tool for the study of solids. Upon laser excitation, carrier multiplication and lattice acceleration beyond thermal velocity can occur, as a result of far-from-equilibrium carrier relaxation.…
We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We restrict our attention to states where one atom is excited and the other is in the ground state, in…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
We show that the electromagnetic moments of unstable particles (resonances) have an absorptive contribution which quantifies the change of the particle's lifetime in an external electromagnetic field. To give an example we compute here the…
We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
The f-sum rule is introduced and its applications to electronic and vibrational modes are discussed. A related integral over the intra-band part of sigma(omega) which is also valid for correlated electrons, becomes just the kinetic energy…
As soon as Lyman or Balmer lines overlap, the net absorption cross section rapidly approaches the value at the series limit. Independent of the difficult question of the relative contributions of line and continuous opacity, we can get a…
We derive general properties, which hold for both quantum and classical systems, of response functions of nonequilibrium steady states. We clarify differences from those of equilibrium states. In particular, sum rules and asymptotic…
We shall show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. More exactly, we give summation formula for the general hyperharmonic series.
The spontaneous emission of radiation of metallic electrons embedded in a high-intensity enhanced surface plasmon field is considered analytically. The electrons are described by exact dressed quantum states which contain the interaction…