Diffusion in a weakly random Hamiltonian flow
نویسنده
چکیده
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves undergoes a spatial diffusion.
منابع مشابه
Energy Transfer in a Fast-slow Hamiltonian System
We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a non linear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weak...
متن کاملRandom Perturbations of 2-dimensional Hamiltonian Flows
We consider the motion of a particle in a periodic two dimensional flow perturbed by small (molecular) diffusion. The flow is generated by a divergence free zero mean vector field. The long time behavior corresponds to the behavior of the homogenized process that is diffusion process with the constant diffusion matrix (effective diffusivity). We obtain the asymptotics of the effective diffusivi...
متن کاملRandom Iteration of Maps on a Cylinder and diffusive behavior
In this paper we propose a model of random compositions of maps of a cylinder, which in the simplified form is as follows: (θ, r) ∈ T×R = A and f±1 : ( θ r ) 7−→ ( θ + r + εu±1(θ, r). r + εv±1(θ, r). ) , where u± and v± are smooth and v± are trigonometric polynomials in θ such that ∫ v±(θ, r) dθ = 0 for each r. We study the random compositions (θn, rn) = fωn−1 ◦ · · · ◦ fω0(θ0, r0) with ωk ∈ {−...
متن کاملOne-dimensional classical diffusion in a random force field with weakly concentrated absorbers
A one-dimensional model of classical diffusion in a random force field with a weak concentration ρ of absorbers is studied. The force field is taken as a Gaussian white noise with 〈φ(x)〉 = 0 and 〈φ(x)φ(x)〉 = g δ(x− x′). Our analysis relies on the relation between the FokkerPlanck operator and a quantum Hamiltonian in which absorption leads to breaking of supersymmetry. Using a Lifshits argument...
متن کاملDiffusion and Mixing in Fluid Flow
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time, provided that the flow amplitude is large enough. The necessary and sufficient condition on such flows is expressed naturally ...
متن کامل