This proposed workshop is the sixth of a series that started in 2004. It takes place in combination with a school on the same topic (time-dependent density-functional theory, TDDFT), at the "Centro de Ciencias de Benasque Pedro Pascual" ("Pedro Pascual Benasque Center for Science"), in the village of Benasque, Spain. The idea is to have a school first, in which a very intense introduction to the theory, practice, and numerical implementation of TDDFT. Then, the workshop covers all the main aspects by the leading experts, which includes most of the school teachers. All the students of the school are expected to participate in the workshop, in order to learn about the state-of-the-art of the subject, after being exposed to the fundamentals.

This combination of events has proved to be very fruitful, and has motivated us to continue the series, with bi-yearly periodicity. Since TDDFT is a rapidly evolving field of Science, the precise content of both school and workshop have changed over the years - although the format of the events has been largely unaltered.

Spectroscopies are the tools used to study the microscopic structure of matter. The experimental results obtained with these tools can only be interpreted correctly with the help of accurate theoretical methods, capable of simulating the microscopic behavior of matter subject to external perturbations. A number of spectroscopic methods address electronic excited states (e.g. optical absorption spectroscopy, photo-electron emission spectroscopy, etc), and hence the need of first principles theoretical methods capable of addressing the excited state many-electron problem. Time-dependent density-functional theory (TDDFT) is one of such methods.

It can be viewed as an extension of density functional theory (DFT) to time-dependent problems, and as an alternative formulation of time-dependent quantum mechanics. The basic rationale behind DFT is the reformulation of the many-electron problem (roughly speaking, an equation with 3N variables, where N is the number of electrons) as a problem whose basic variable is the one-particle density, an object depending on the three spatial variables. Alternatively, we can view DFT as a manner to tackle with the interacting many-electron problem by studying a much easier non-interacting one (since in almost all cases it is the Kohn-Sham formulation of DFT that is used). TDDFT is based on the same reduction of complexity. The advantages are clear: a complex function in 3N-dimensional space is replaced by a real function that depends solely on a 3-dimensional vector - the density. Usually this 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.

TDDFT is by no means the only approach to the excitations of many-electron systems. In fact, more accurate (yet more expensive) techniques (based on many-body perturbation theory, for example) exist, and therefore these alternatives will also be covered in both the workshop and the school, in particular their relation and comparison to TDDFT. However, TDDFT achieves a good balance between accuracy and computational cost. In consequence, its use 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...). All these possibilities add up to the scientific success of TDDFT: this topic has had a major impact, for example, in the recent Psi_k 2010 Conference, and it also has dedicated sessions in all major conferences (DPG, APS, etc). Therefore, there is a clear demand for this School & Workshop as it provides to the students with the state of the art in the field from from the basics to the latest developments.