No abstract

No abstract

No abstract

No abstract

It is shown that a system of coupled harmonic oscillators can be made a model of a heat bath. Thus a particle coupled harmonically to the bath and by an arbitrary force to a fixed center will (in an appropriate limit) exhibit Brownian motion. Both classical and quantum mechanical treatments are given.

No abstract

We will consider a very simple stochastic model, a random walk. Unfortunately, this model is little known. It has very interesting features and leads not to a diffusion equation but to a hyperbolic one. The model first appeared in the literature in a paper by Sidney Goldstein, known to you mostly because of his work in fluid dynamics. The model had first been proposed by G. I. Taylor -I think in an abortive, or at least not very successful, attempt to treat turbulent diffusion. But the model itself proved to be very interesting.The problem is the following: Suppose you have a lattice of points. I mean discrete, equidistant points as in Figure 1.

No abstract