Related papers: Fokker-Planck-Rosenbluth-Type Equations for Self-g…
We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a non-cosmological context, by…
Within the general framework of $f(R)$ gravity, we introduce a function of the electromagnetic curvature invariant $f(\mathbb{F})$ that couples minimally to gravitation to ensure a consistent treatment of curvature functions in these…
We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is…
In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the…
From a given Fokker-Planck equation, a multi-parameter deformed partner Fokker-Planck equation is constructed. This is done by first deleting a set of eigenstates of the original FPE by the multi-step Darboux-Crum transformation, and then…
Particle acceleration by turbulence plays a role in many astrophysical environments. The non- linear evolution of the underlying cosmic-ray spectrum is complex and can be described by a Fokker-Planck equation, which in general has to be…
The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including…
We derive non-linear stochastic Fokker-Planck equation from stochastic systems particles with individual and environmental noise via relative entropy method, with pathwise quantitative bounds. Moreover, we prove the existence of a unique…
This paper aims to explore non-Markovian dynamics of nonlinear dynamical systems subjected to fractional Gaussian noise (FGN) and Gaussian white noise (GWN). A novel memory-dependent Fokker-Planck-Kolmogorov (memFPK) equation is developed…
Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini…
Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or by a Fermi pencil-beam equation. We present a rigorous approximation analysis of these three models…
In this work we introduce two different generalizations of the Fokker-Planck equation in (1+1) dimensions by replacing the spatial derivatives in terms of generalized Dunkl-type derivatives involving reflection operators. As applications of…
We use the Schr\"odinger--Newton equation to calculate the regularized self-energy of the particle using a regular self-gravitational and electrostatic potential derived in the string T-duality. The particle mass $M$ is no longer…
We provide an overview of the Gross-Pitaevskii-Poisson equation (GPPE) that is used to model self-gravitating superfluid systems, which include gravitationally collapsed boson and axion stars and dark-matter haloes. We outline how this…
We consider $N$ uniformly-accelerating Unruh-DeWitt detectors whose internal degrees of freedom are coupled to a massless scalar field in $(1+1)$D Minkowski space. We use the influence functional formalism to derive the Langevin equations…
The general relativistic corrections in the equations of motion and associated energy of a binary system of point-like masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the…
Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio $m/M$. The corresponding Langevin equation contains nonlinear corrections to the…
The aim of this work is to formulate two new solutions by decoupling the field equations via a minimal geometric deformation in the context of self-interacting Brans-Dicke gravity. We introduce an extra source in the anisotropic fluid…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…
Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive…