Related papers: Real diffusion with complex spectral gap
Diffraction gratings synthetically moving at trans-luminal velocities contain points where wave and grating velocities are equal. We show these points can be understood as a series of optical event horizons where wave energy can be trapped…
This paper deals with the spectral densities of a dispersive dielectric object in the framework of macroscopic quantum electrodynamics based on the modified Langevin noise formalism. In this formalism, the electromagnetic field in the…
In this note we consider a relativistic heavy quark which moves in the quark-gluon plasmas. By using the holographic methods, we analyze the Langevin diffusion process of this relativistic heavy quark. This heavy quark is described by a…
The advent of Generative Adversarial Network (GAN) architectures has given anyone the ability of generating incredibly realistic synthetic imagery. The malicious diffusion of GAN-generated images may lead to serious social and political…
We consider Wong equations for a particle with a continuous mass spectrum in a random Yang-Mills field approximating the quantum field at finite temperature. We show that particle time evolution can be approximated by a relativistic…
Diffusive Radiation is a new type of radiation predicted to occur in randomly inhomogeneous media due to the multiple scattering of pseudophotons. This theoretical effect is now observed experimentally. The radiation is generated by the…
We carry out an study of the Brox diffusion with killing. It turns out that when leaving fixed the environment one is able to recast some theory of diffusion and differential operators to deal with the ill-posed generator of the Brox…
We study the semigroup of the symmetric $\alpha$-stable process in bounded domains in $\R^2$. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This…
The growing demand for effective spectrum management and interference mitigation in shared bands, such as the Citizens Broadband Radio Service (CBRS), requires robust radar detection algorithms to protect the military transmission from…
We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the particle can be instantaneously…
A high energy power law is a common feature in the spectra of many astrophysical objects. We show that the photons in a relativistic plasma with a variable Lorentz factor go through repeated scattering with electrons to gain energy. The…
Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…
Subdiffusive behavior of one-dimensional stochastic systems can be described by time-subordinated Langevin equations. The corresponding probability density satisfies the time-fractional Fokker-Planck equations. In the homogeneous systems…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam…
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…
Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of…
The probability distribution effectively sampled by a complex Langevin process for theories with a sign problem is not known a priori and notoriously hard to understand. Diffusion models, a class of generative AI, can learn distributions…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…