A combination of experiments and theory has enabled physicists to understand the diffusion of individual atoms in periodic systems for the first time. The interactions of individual atoms with light at ultralow temperatures close to absolute zero provide new insight into ergodicity, the fundamental principle of thermodynamics.
Diffusion refers to a universal physical phenomenon which describes the movement of particles in their surroundings, which can be solid, liquid or gas. The first investigations by Robert Brown and the corresponding explanations by Albert Einstein were made more than a century ago. Robert Brown observed the random, irregular movements of pollen in a fluid. Einstein and Smoluchowski correctly interpreted this ‘Brownian motion’ as the result of random collisions of fluid molecules with the pollen. Diffusion in complex systems goes a step further and can have a variety of characteristics: tumour movements in living organisms, DNA transport in cells, ion movements in batteries, atomic movements on surfaces – these are all diffusion processes in complex systems. There is great interest in interpreting the underlying mechanisms, which could one day extend to everyday applications. Physical experiments using ultracold atoms provide insight into diffusion in periodic structures which are relevant for a wide range of complex systems.
Physicists at TU Kaiserslauten, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) and Kyoto University in Japan have taken an important step in understanding the foundations of complex diffusion and interpreting their experimental data. For the study, which was published in the renowned journal Nature Physics, the team from Kaiserslauten led by Professor Artur Widera (Faculty of Physics and State Research Centre OPTIMAS) developed a novel model system: an individual atom is cooled almost to absolute zero using lasers and caught in a trap of light in a nearly-perfect vacuum. The atom is then put in an environment created by a light field in which atoms’ light absorption and light emission function as collisions with another particle. In this environment diffusion can be set as desired and the movements of the atom can be observed via camera. Parallel to this development, theoretical physicists at FAU and Kyoto developed a model to described the dynamics of the system. The central focus of this process was understanding processes in respect of the physical quantity of ergodicity. Thanks to the excellent coordination of the experiment and theory, diffusion processes can now be understood beyond Brownian motion. In future these results may have an influence on scientists’ understanding of a range of complex systems in medicine, biology, physics and technology.
Foundations of diffusion
The movements of individual cells in the body or the transport of charge carriers in energy stores can only be understood in connection with their environments. The particles in these environments constantly collide with cells or charge carriers, thus influencing their movements. In many cases these processes can be described as Brownian motion using Einstein’s theory. Sometimes observations cannot be described with this model and it is not yet possible to identify non-Brownian motion in systems at first glance. The researchers at the three universities have succeeded in theoretically and experimentally demonstrating how diffusion can be characterised in certain complex systems.
Ergodicity as a key to understanding complex diffusions
A key aspect of the studies was investigating the atomic system on time scales relevant for the establishment of ergodicity. Ergodicity is the foundation of thermodynamics and is an important quantity for describing diffusion processes. Put simply, the ergodic hypothesis states that the movement of an individual particle in a group of particles is representative of all the particles. This hypothesis generally underlies all phenomena observed in our daily life. However, for most systems it only applies over very long periods of time. In their study the researchers have shown that even diffusion processes which appear ‘normal’ in certain cases can contradict the ergodic hypothesis over surprisingly long periods of time. These results have interesting consequences for researchers’ understanding of diffusion in complex systems and can help to re-evaluate and interpret observations and measurements in biological systems.