Statistical Physics, Quantum Mechanics, and Complex Systems
Systems composed of a large number of particles or elements can give rise to complex unexpected behaviour and totally new emergent collective properties. Statistical Physics deals indeed with systems composed of many interacting degrees of freedom. Starting from microscopic models, it can describe and predict these unexpected behavior on a large scale, in which collective effects are more than the sum of the properties of the individual constituents. The research at SMFI deals with topics at the borders of Statistical Mechanics, Quantum Mechanics and Condensed Matter Physics, with a strong interdisciplinary content from Biology and Social Sciences. In our research topics, classical and quantum complexity emerges from networks of interactions with non-trivial geometric and dynamical properties. We deal with synchronisation of classical and quantum units, dynamical processes on complex temporal networks, quantum control and complex transport phenomena.
For more information:
Prof. Raffaella Burioni
Prof. Sandro Wimberger
Networks and graphs are the most general mathematical description of a set of elements connected pairwise by a relation. Therefore, it is not surprising that graph theory has been successfully
Complex systems and their modeling are interesting simply because matter is typically complex. On small scales, quantum mechanics describes interactions and dynamics. One typical example of a complex quantum system are photosynthetic molecules (complexes) in which transport properties seem to be governed by quantum mechanical interference. Strong correlations between the constituents make even "small" systems very complicated. In the helium atom, for instance, classical three-body chaos turns into complicated ionization spectra. The modern experimental tools of atom optics allow for a bottom-up construction of strongly correlated many-body quantum systems. We are studying their behavior on the level of single atoms and their interaction. Ongoing collaborations with experimental groups the world over enrich our research on fundamental aspects of quantum transport and its control in view of applications in atomtronics and quantum information.
How does matter diffuse in a complex material? How is information transmitted in a complex network, can a disease spread over an entire population? These are typical non equilibrium questions that we ask in our research. The effect of large fluctuations on these processes is extremely important. In particular, complex systems can often experience Big Jumps, that is sudden huge events that can complete shift the non equilibrium process. Identifying these events and develop a mathematical framework to deal with them is what we do.