Energy Transfer and Joint Diffusion

@article{PajorGyulai2010EnergyTA,
  title={Energy Transfer and Joint Diffusion},
  author={Zsolt Pajor-Gyulai and Domokos Sz{\'a}sz},
  journal={Journal of Statistical Physics},
  year={2010},
  volume={146},
  pages={1001-1025}
}
A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and interacting with each other via elastic collisions. For this model the diffusive limit of the two trajectories is a mixture of joint Gaussian laws (analogous behavior is expected for the mechanical model of two Lorentz disks). 

Billiard Models and Energy Transfer

For two (or more) interacting classical particles the existing few results (for diffusion or energy transfer, for instance) assume that the mass of one of them as compared to the other mass becomes

Infinite measure mixing for some mechanical systems

What mathematical billiards teach us about statistical physics

We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billiards to some fundamental problems of statistical physics and their mathematically rigorous derivations

Number of distinct sites visited by a random walk with internal states

In the classical paper of Dvoretzky and Erdős (Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp 353–367, 1951), asymptotics for the expected value and the

Weak convergence of random walks conditioned to stay away

Let $\{X_n\}_{n\in\mathbb{N}}$ be a sequence of i.i.d. random variables in $\mathbb{Z}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on $[0,1]$ for which $Y_n(k/n)=S_k/\sqrt{n}$

A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1

References

SHOWING 1-10 OF 29 REFERENCES

Joint diffusion on the line

For a one-dimensional system of particles with elastic collisions the trajectories of distinct particles are considered in the diffusion limit. If the initial distance of two particles increases in

Diffusion in a Periodic Lorentz Gas

Self-diffusion in a Lorentz gas on a triangular lattice is studied both analytically and numerically. A simple estimate for the diffusion coefficient, based on the idea of a random walk between

On the Boltzmann equation for the Lorentz gas

We consider the Boltzmann-Grad limit for the Lorentz, or wind-tree, model. We prove that if ω is a fixed configuration of scatterer centers belonging to a set of full measure with respect to the

Self-diffusion for particles with stochastic collisions in one dimension

Color diffusion in a classical fluid composed of two species differingonly by color is intimately connected with the asymptotic behavior of trajectories of test particles in the equilibrium system.

Limit theorems for locally perturbed planar Lorentz processes

Let us modify the scatterer configuration of a planar, finite-horizon Lorentz process in a bounded domain. Sinai asked in 1981 whether for the diffusively scaled variant of the modified process

Recurrence properties of planar Lorentz process

First return and first hitting times, local times and first intersection times are studied for planar finite horizon Lorentz processes with a periodic configuration of scatterers. Their asymptotic

Statistical properties of lorentz gas with periodic configuration of scatterers

In our previous paper Markov partitions for some classes of dispersed billiards were constructed. Using these partitions we estimate the decay of velocity auto-correlation function and prove the

Heat conduction and Fourier's law by consecutive local mixing and thermalization.

We present a first-principles study of heat conduction in a class of models which exhibit a new multistep local thermalization mechanism which gives rise to Fourier's law. Local thermalization in our

Random walk in an inhomogeneous medium with local impurities

In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ℤd (d=2) can drastically change if local impurities are present, it is shown that local