Related papers: Fokker-Planck-Rosenbluth-Type Equations for Self-g…
The fractional Fokker-Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., $\mathbf{13}$, 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the…
Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…
$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasi-static approximation and sub-Hubble…
An integral relation is derived from the Fokker-Planck equation which connects the steady-state probability currents with the dynamics of relaxation on short timescales in the limit of small perturbation fields. As a consequence of this…
In this paper new multi-variable deformed Fokker-Planck (FP) equations are presented. These deformed FP equations are associated with the Ruijsenaars-Schneider-van Diejen (RSvD) type systems in the same way that the usual one variable FP…
We consider the Fokker-Planck equation with a strong external magnetic field. Global-in-time solutions are built near the Maxwellian, the global equilibrium state for the system. Moreover, we prove the convergence to equilibrium at…
After a brief review of the first phase of development of Quantum-Gravity Phenomenology, I argue that this research line is now ready to enter a more advanced phase: while at first it was legitimate to resort to heuristic order-of-magnitude…
We interpret a class of nonlinear Fokker-Planck equations with reaction as gradient flows over the space of Radon measures equipped with the recently introduced Hellinger-Kantorovich distance. The driving entropy of the gradient flow is not…
We derive new terms in the post-Newtonian (PN) expansion of the generalized redshift invariant $\langle u^t \rangle_\tau$ for a small body in eccentric, equatorial orbit about a massive Kerr black hole. The series is computed analytically…
Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the…
For the nonlinear Fokker--Planck equation $$\partial_tu = \Delta\beta(u)-\nabla \Phi \cdot \nabla \beta(u) - div_{\varrho}\big(D(x)b(u)u\big),\quad (t,x) \in (0,\infty)\times \mathbb{R}^d,$$ where $\varrho = \exp(-\Phi)$ is the density of a…
We study both analytically and numerically the gravitational fields of stars in f(R) gravity theories. We derive the generalized Tolman-Oppenheimer-Volkov equations for these theories and show that in metric f(R) models the Parameterized…
For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time…
The Fokker_Planck equation can be derived in a consistent manner through a microscopic approach based on a unified scheme of classical and quantum mechanics. Here we shall derive it through a purely quantum mechanical approach based on the…
The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGF) or reduced density matrix methods. Approximations are introduced…
As is known, in modified cosmological theories of gravity many of the cosmologies which could not be generated by standard Einstein gravity, can be consistently described by $F(R)$ theories. Using known reconstruction techniques, we…
We perform a post-Newtonian (PN) solar system analysis for Palatini $f(R)$ theories considering finite volume non-spherical planets and with emphasis to $f(R)$ functions that are analytical about $R=0$. First we consider the Will-Nordtvedt…
Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric…
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…
We consider the relativistic, spatially inhomogeneous Fokker-Planck equation with an external confining potential. We prove the exponential time decay of solutions towards the global equilibrium in weighted $L^2$ and Sobolov spaces. Our…