Ballastic and Diffusive motions

The impacts of heat bath on a small system embedded in it are clear on macroscopic and stationary scale, but they remain a challenging subject from the microscopic and dynamic point of view. A simple example is the Brownian motion of a single particle placed in a air or other medium. The equilibrium statistical theory was forwarded by Einstein a century ago, yet what actually take place over very short periods are still under intensive study (see previous entries). Here comes a new report [Science, 332:802(2011)]:

For many years after Einstein's contributions, it was expected that the transition from ballistic to diffusive motion would be quite sharp, corresponding to an exponential decay of the particle's memory of its earlier velocity. However, about 50 years ago, hints from computer simulations and theory started to suggest a more complex scenario. In particular, hydrodynamic vortices in the liquid created by the particle's motion lead to memory effects, and the particle's velocity decays much more slowly than exponentially, exhibiting a t^−3/2 “long-time-tail” (12). Detailed analysis by Huang et al. of data like that shown in the second figure, panel B, where the ballistic-to-diffusive transition spans more than three decades in time, has now provided a thorough verification of the full, complicated hydrodynamic theory (13, 14). Although several previous experiments had observed the breakdown of the simple diffusion picture [e.g., (15)], the present studies extend into the ballistic regime.

What next? Li et al. mention the fascinating prospect of laser cooling a trapped particle to a temperature at which quantization of the energy of this mesoscopic object could be observed (16). Huang et al. suggest extending their measurements to Brownian motion in confined regions and heterogeneous media. Here, understanding the details of prediffusive motion over subnanometer distances could well be relevant to some biological processes, such as the lock-and-key mechanism of enzyme action.