October 19, 2011
Glowing Beacons Reveal Hidden Order In Dynamical Systems
Experimental confirmation of a fundamental physical theorem
The so-called ergodic theorem formulates a fundamental physical principle relating to the behavior of dynamical systems. Essentially the theorem states that in a multiparticle system each individual particle behaves just as “chaotically” as does the system as a whole. In other words, one can extrapolate from the behavior of a single element to that of the whole system. Strangely enough, in spite of its wide-ranging implications, the theorem has not been rigorously tested experimentally. A collaborative effort mounted by Professor Christoph BrÃ¤uchle´s team in the Department of Chemistry at LMU Munich and Professor JÃ¶rg KÃ¤rger´s group at Leipzig University has now confirmed the validity of the theorem by measuring the diffusive behavior of ensembles of particles and the trajectories of single molecules in the same system. Using fluorescent molecules as tracers and high-resolution imaging methods, the LMU investigators were able to track the paths of individual molecules, while the Leipzig group studied the collective behavior of the whole ensemble. “It will be very interesting to take a closer look at systems that do not conform to the tenets of the ergodic theorem and to determine the reasons for their aberrant behavior,” says BrÃ¤uchle.
This still leaves one problem to be solved - successful application of the two methods requires very different, indeed apparently conflicting, conditions. NMR measurements need high concentrations of molecules with large diffusion coefficients, while single-molecule spectroscopy works best with extremely dilute solutions of species with small diffusion coefficients. By using particular organic dyes with high fluorescence yields in combination with porous silicate glasses containing networks of nanometer-sized channels in which the dye molecules can diffuse, the researchers were able to create conditions that were compatible with both methods. This experimental set-up allowed them to perform single-molecule and ensemble measurements on the same system.
When the two teams compared their data, they found that the diffusion coefficients (the parameter that describes diffusive motion) obtained by the two techniques agreed with each other — providing the first experimental confirmation of the ergodic theorem in this context. The next step will be to examine systems in which the theory does not apply. “The diffusion of nanoparticles in cells looks like an interesting example,” says BrÃ¤uchle, “and for us the important thing is to find out why the ergodic theorem doesn´t hold in this case.”
The project in Munich was carried out under the support of the Cluster of Excellence “Nanosystems Initiative Munich” (NIM) and DFG Priority Program 749 (Dynamics and Intermediate Molecular Transformations), while the work in Leipzig was supported by the DFG as part of Research Unit 877 (From Local Constraints to Macroscopic Transport). (gÃ¶d/PH)
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