Related papers: A brief introduction to dispersive methods
Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…
We briefly expose some key aspects of the theory and use of dispersion models, for which Bent Jorgensen played a crucial role as a driving force and an inspiration source. Starting with the general notion of dispersion models, built using…
We consider power-behaved contributions to hard processes in QCD arising from non-perturbative effects at low scales which can be described by introducing the notion of an infrared-finite effective coupling. Our method is based on a…
Different theoretical methods used for the description of diffractive processes in small-x deep inelastic scattering are reviewed. The semiclassical approach, where a partonic fluctuation of the incoming virtual photon scatters off a…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
This work reports the conditions under which weak scattering assumptions can be applied in a beam loaded by multiple resonators supporting both longitudinal and flexural waves. The work derives the equations of motion of a one-dimensional…
An old problem in mathematical physics deals with the structure of the dispersion relation of the Schr\"odinger operator $-\Delta+V(x)$ in $R^n$ with periodic potential near the edges of the spectrum. A well known conjecture says that…
We reexamine several issues related to the physics of scaling in electron scattering from nuclei. A basic model is presented in which an assumed form for the momentum distribution having both long- and short-range contributions is…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…
We survey four instances of the Fourier analytic 'transference principle' or 'dense model lemma', which allows one to approximate an unbounded function on the integers by a bounded function with similar Fourier transform. Such a result…
An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. It is shown that…
We study the one-point and two-point Green's functions in a complex random matrix model to sub-leading orders in the large N limit. We take this complex matrix models as a model for the two-state scattering problem, as applied to spin…
Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method.…
We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident…
We apply a truncated set of dynamical equations of motion for connected equal-time Green functions up to the 4-point level to the investigation of spontaneous ground state symmetry breaking in $\Phi^4_{2+1}$ quantum field theory. Within our…
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
The basics of focused transport as applied to solar energetic particles are reviewed, paying special attention to areas of common misconception. The micro-physics of charged particles interacting with slab turbulence are investigated to…
Using the 1/N_C expansion scheme and truncating the hadronic spectrum to the lowest-lying multiplets of resonances we develop a procedure to implement QCD information on the non-perturbative regime populated by resonances through the use of…