Related papers: A brief introduction to dispersive methods
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…
In this paper we shall discuss the effect of disorder induced configuration fluctuations on single particle and two-particle phonon Green functions in substitutional random binary alloys. The randomness of the system will be dealt within…
We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the…
We show that using the properties of the photon Green's function one can successfully describe the propagation of arbitrary nonclassical optical radiation through structured materials. In contrast to the similar input-output approach, our…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
In this paper, we establish new results for the uniform far-field asymptotics of the two-layered Green function (together with its derivatives) in 2D in the frequency domain. To the best of our knowledge, our results are the sharpest yet…
Using the Green function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input--output…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
Using Schwinger's quantum action principle, dispersion relations are obtained for neutral scalar mesons interacting with bi-local sources. These relations are used as the basis of a method for representing the effect of interactions in the…
We introduce a new method for simulating colloidal suspensions with spherical colloidal particles of dielectric constant different from the surrounding medium. The method uses exact calculation of the Green function to obtain the ion-ion…
The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of…
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular,…
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
A theoretical study on the weak scattering formulation for flexural waves in thin elastic plates loaded by point-like resonators is reported. Our approach employs the Born approximation and far-field asymptotics of the Green function to…
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical…
We propose a new model to approximate the wave response of waveguides containing an arbitrary number of small inclusions. The theory is developed to consider any one-dimensional waveguide (longitudinal, flexural, shear, torsional waves or a…
Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its…