This proposed School is in fact the first half of a combined event: a School or tutorial on TDDFT, immediately followed by a workshop at the same location. For the workshop we are submitting a separate application.

Time-dependent density-functional theory (TDDFT) is an extension of density functional theory (DFT) to time-dependent problems, and can be viewed as an alternative formulation of time-dependent quantum mechanics. As in DFT, the wave-function no longer has the leading role: the basic variable of TDDFT is the one-body electron density. The advantages are clear: a complex function in 3N-dimensional space (where N is the number of electrons in the system) - the many-body wave-function - is replaced by a real function that depends solely on a 3-dimensional vector - the density. Usually the density is obtained using an auxiliary system of non-interacting electrons that feel an effective time-dependent potential, the time-dependent Kohn-Sham potential. Its exact form is, however, unknown, and has to be approximated.

The use of TDDFT is increasing, and it is fast becoming one of the tools of choice to get accurate and reliable predictions for excited-state properties in solid state physics, chemistry and biophysics, both in the linear and non-linear regimes. This interest has been motivated by the recent developments of TDDFT (and time-dependent current functional theory) and include the description of photo-absorption cross section of molecules and nanostructures, electron-ion dynamics in the excited state triggered by either a small or high intense laser fields, van der Waals interactions, development of new functionals coping with memory and non-locality effects, applications to biological systems (chromophores), transport phenomena, optical spectra of solids and low-dimensional structures (as nanotubes, polymers, surfaces...).

Despite the rising interest in the calculation of excited state properties of quantum systems, the techniques being used have usually been just one of the topics covered in international meetings, schools and workshops. This means that scientists new to the field face difficulties in grasping its many aspects that could be alleviated if they could attend a school on time-dependent density functional theory (TDDFT) or Many-Body Techniques (MBT). We also believe that a school on these techniques is extremely helpful for young graduate students, post-docs and even older scientists that are envisaging a project for which TDDFT/MBT would be the tool of choice. For this reason we decided to organize a set of schools and workshops on these techniques, covering its theoretical, practical, and numerical aspects. The first one was done in Benasque in 2004, and continued in 2006, 2008, and 2010.

A clear demonstration of the impact of these events is the publication of a Springer Lecture Notes book with the contributions from the first school. This book was the first comprehensive review of the field to be published. A copy of this book was offered to all participants in the 3rd event, and served as basic course material for the school. We plan to repeat this in the next event. At the end of the four schools we conducted a survey among the students to get their impression on the contents of the school, the lectures and practical sessions. The input was very positive, in particular concerning the idea of having this combined event repeated in the future. A two-year periodicity seemed to be ideal.

Following our previous experience, we are convinced that the most efficient scheme for training of young researchers in these techniques is to have a school where the basic theory is taught followed by a workshop that introduces them to the forefront research in the field. The school should have an equal share of theoretical and practical classes. This eases the learning of the techniques and provides the students with the practical knowledge of the numerical aspects and difficulties, at the same time introducing them to well-established open source numerical codes. At the end of the school, students should have sufficient working knowledge to pursue their projects at their home institution.

The school is followed by an international workshop, where the new developments of TDDFT and Many-Body Techniques for the calculation of excitations are discussed. Students attending the school are encouraged to attend the workshop, so they can get in contact with state of the art research in the field. The purpose of the workshop is to bring together leading experts in all these fields with different backgrounds, like density functional, many-body, nuclear physics, quantum chemists, and biophysicists. This allows the exchange of ideas between the different fields and the creation of links between the traditionally separated communities. We believe that the intense and informal discussion which is possible in this kind of workshops can contribute to the formation of a strong community in the field of TDDFT.

The call for participation will be mainly directed to students and scientists specialized on computational physics, quantum chemistry and biophysics. We will limit the number of students in the school to 50 and participants to the workshop to less than 120, in order to ensure a maximum interaction between all the scientists participating. Attendance of graduate students and postdocs will be strongly encouraged through the inclusion of short contributed talks and a poster session. Furthermore, the two best posters at the school will be awarded with short oral presentations at the workshop.