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A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the…
In recent years, gravitational models motivated by quantum corrections to gravity which introduce higher order terms like $R^{2}$ or terms in which the Riemann tensor is not symmetric have been studied by several authors in the form of a…
We derive an effective equation and action for comoving curvature perturbations and gravitational waves (GWs) in terms of a time, momentum and polarization dependent effective speed, encoding the effects of the interaction among metric…
In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
The paper is devoted to the problem of the determination of regular and thermal forces acting on microscopic and smaller objects in fluids. One of the methods how regular forces are determined is the measurement of the drift velocity of…
There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuation-dissipation relation easily gets modified and the mobility matrix is no…
We investigate the relation between mobility and diffusivity for Brownian particles under steady shear near the glass transition, using mode coupling approximations. For the two directions perpendicular to the shear direction, the particle…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…
Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point…
We consider Dyson Brownian motion for classical values of $\beta$ with deterministic initial data $V$. We prove that the local eigenvalue statistics coincide with the GOE/GUE in the fixed energy sense after time $t \gtrsim 1/N$ if the…
We present the exact analytical equation of diffusion-mobility for two-dimensional (2D) Schr\"odinger type transport systems, from molecules to materials. The density of electronic states in such Schr\"odinger systems pertains to the 2D…
We study the motion of Brownian particle in modulated media in the strong damping limit by using {\em toy model}, with special emphasis on the transition from localise to diffusive behavior. By using model potential we have seen the…