Time evolution of fermionic systems from first principles

Nuclei are minute objects at the center of atoms, formed by several neutrons and protons, bound together by the strong interaction. Elements are defined according to their number of protons, while different isotopes of an element are specified by their number of neutrons. Some combinations of neutrons and protons yield isotopes which are stabler than others. Of the around 3000 isotopes observed so far, only about 280 of them are stable. The rest, unstable (radioactive) nuclei, decay with a characteristic time that shortens significantly as the proton and neutron content of a nucleus moves away from the stable conditions. Several unstable isotopes have actually not been measured yet: some models predict that about 3000 more of them might actually exist. So what does this have to do with us? Even though you might think that such uncommon nuclei have little impact on our world, it turns out that they play a basic role. Exotic isotopes are formed continuously in stars and they are the seeds from which all the remaining nuclei, including the stable ones, are formed. Ultimately, isotope science teaches us about the stuff we are made of. The 2010s are going to be a particularly exciting decade for nuclear physics. Extremely unstable atomic nuclei will be created soon in research laboratories that are being built in France, Germany, Japan or the US as part of a coordinated worldwide effort to reach the limits of nuclear stability. With the valuable experimental data collected in these facilities, theorists like me will be able to understand better how nuclei behave. This is a very challenging task, because quantum physics is involved and everyday intuition often fails when applied to nuclei. As a matter of fact, experience shows that extrapolating from trends of known isotopes is not enough to understand the unfamiliar phenomena occurring in exotic nuclei. Nuclear physics is thus facing an unknown territory, an uncharted area of the isotope chart. As in every exploration, the most advanced technology is required to proceed securely through untraveled lands. For nuclear physics, theoretical models to describe reaction with exotic isotopes need critical improvements. A key issue is predictability: present models are generally based on a series of parameters which are typically derived from stable nuclei. Extending these models to exotic isotopes can introduce uncontrolled errors and undermine the predictive power of theoretical models. An alternative is to try to start from as few ingredients and parameters as possible: only basic constituents (neutrons and protons), the interaction between them and a quantum many-body theory to account for the presence of all the particles in the system. My research proposal is aimed in this direction. Using a quantum mechanical time-dependent approach, I would like to simulate collisions of nuclei directly in the computer, by solving a set of equations that simultaneously describe the structural properties of the isotopes as well as their evolution in time. The non-equilibrium Green's functions techniques that I would like to work on are currently being developed to study other systems (nanodevices, molecules, plasmas), but their broad number of potential applications make them perfect candidates for the description of nuclear collisions. The power of physics lies in its ability to describe very different systems with the same tools. Quantum mechanical time-evolving algorithms, however, are rather challenging from the computational point of view. I will need to develop new numerical techniques and use powerful computers to carry the project on successfully. A particularly curious issue related to Green's functions techniques is that they introduce the so-called memory effects. What this means, in practice, is that the simulated elements need to remember their past in order to project their future: just as we humans should do from time to time!