相关论文: On summation of Kapteyn series
To describe the nonequilibrium states of the system, a new thermodynamic parameter - system lifetime - is introduced. Statistical distributions that describe the behavior of energy and lifetime are recorded. Entropy and obtained…
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is…
We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.
Collective electronic excitations "excitons" in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. Excitons for long wave numbers and…
The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is…
In super- or subradiance, a quantum superposition of excited atoms collectively emits a photon much more or much less rapidly than an isolated atom. Superradiant and subradiant lifetimes have been derived for finite spheres of uniform…
Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition…
On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is…
We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…
We investigate the period function of $\sum_{n=1}^\infty\sigma_a(n)\e{nz}$, showing it can be analytically continued to $|\arg z|<\pi$ and studying its Taylor series. We use these results to give a simple proof of the Voronoi formula and to…
It is shown that the addition of a non-linear term to the Lagrangian of the electromagnetic field yields a fluid with an asymptotically super-negative equation of state, causing an accelerated expansion of the universe. Some general…
This paper studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is…
The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and…
New techniques for evaluating the closed time path action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of warm inflation…
In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an…
We present explicit expressions for the high-frequency asymptotic behavior of electron self-energy of general quantum impurity models, which may be useful for improving the convergence of dynamical mean-field calculations and for the…
During the last decade, significant progress has been achieved in the rapidly growing field of the dynamics of {\it hot} carriers in metals. Here we present an overview of the recent achievements in the theoretical understanding of electron…
The work examines the effect of multiple photon emission on the quantum mechanical state of an electron emitting synchrotron radiation and on the intensity of that radiation. Calculations are done with the variant of perturbation theory…
We derive an effective Dicke model in momentum space to describe collective effects in the quantum regime of a free-electron laser (FEL). The resulting exponential gain from a single passage of electrons allows the operation of a Quantum…
The process of Compton scattering by a free electron with subsequent reemission of one or two photons is considered in the assumption of finite interaction time. The corresponding cross sections are obtained in the framework of relativistic…