School

The first week was organized as a school for mature students, postdocs, and young researchers. There were four lecturers, each giving three lectures of one hour, and a follow up of twice two hours of discussion and exercise sessions. This resulted in four full days of teaching activities. The topics and teachers were chosen to present a broad pedagogical introduction to the subjects expected at the workshop, namely momentum and coordinate space few-body techniques, the concept of universality, and the transition from few- to many-body degrees of freedom. The lecture notes by the teachers were made available before the presentations.

The last day was reserved for the contributions of the participants. Each of them had twenty minutes to present a project he had himself chosen and respond to questions. The organizers were present at all lectures and talks on the last day of the school. It was a good surprise that the talks by the participants were of very high quality both by their scientific content and pedagogical aspects.

The school participants were asked to evaluate the lectures and the exercises, through an e-mail ques- tionnaire. The responses were in general very positive with evaluations ranging from excellent to above the average. Without exceptions, the responses indicated that the school was a very fine prepa- ration for the specialized workshop talks. Also the individual project presentations and the subsequent discussions on the last day were unanimously very positively received. The lectures were deemed very well presented while the exercises in general were less popular and less helpful probably because they were too often made at generalizations and further applications of the concepts introduced in the lec- tures, and less often devoted to immediate and direct applications. The amount of content in the four series of lectures probably added up to be too large for four days. The week was intense but overall the participants were satisfied.

Workshop

The second week was organized as a workshop with 39 contributions of 40 minutes by all participants split as 30 minutes for the talk and 10 minutes for the discussion. In addition, the Colloquium by the recipient of the Gutzwiller award was included in the program of the workshop. The 9 groups of topics, 1. Universality, 2. Finite-range corrections, 3. Few and many-body degrees of freedom, 4. One and two dimensions, 5. Dimensional crossover, 6. Multicomponent systems, 7. Dynamics, 8. Reactions with weakly bound systems, 9. Mathematical few-body problems. All topics received attention through several talks.

Most workshop contributions are planned to appear in a special issue of Few-Body Systems entitled “Special issue on Critical Stability of Quantum Systems” where also the lectures at the school will be included.

There were 63 participants at the workshop, coming from 17 different countries, including almost all 21 school participants who stayed for the workshop. A number of subfields of physics with focus on few-body quantum problems were represented, such as quantum chemistry, mathematical, atomic, molecular, condensed matter, hadron and nuclear physics. Apart from the school participants (very young) and the organizers (rather senior) the average age of the workshop participant was about 43 years. This corresponds to a generation ready to take over from the very well established physicists. They all presented convincing and mature talks about the diverse topics they had been working on, expressing vitality and new avenues to be explored on the boundaries and within the different subfields of physics.

The topics of universality in various disguises were probably the most prominent issue discussed at the workshop. It is not easy to select specially interesting contributions, but if pressed consensus probably would be, (i) the experiments by Reinhard Do ?rner where the probability distribution of the excited atomic helium trimer is mapped out, (ii) the zoo of Efimov towers of excited states by Yusuke Nishida, (iii) the topological classification of symmetries of few-body structures in different spatial dimensions by Nathan Harsmann.

The overall goals of the workshop were achieved, that is exchange of ideas and techniques across the barriers of subfields, updating and distributing research results, and initialization of new collaborations perhaps based on the ideas exchanged at the meeting. The school served both as basic education but also as a preparation for the more specialized workshop talks.

The organizers are plainly satisfied by the success of the school and workshop, which came across different subfields of physics and in broad sense each with its set of concepts applied to finite and many-body quantum systems in different dimensions. At the workshop the underlying relevance of the long range quantum correlations brought by some selected degrees of freedom to the complex finite or infinite quantum systems were tackled in the presentations. This common universal basic concept, was raised in different forms during the discussions through the fruitful questions and answers, where the participants were prompted to make an effort to go over distinctions and find the subtle links between the conceptual complexity coming across the boundaries of different subfields of physics.

All this was made possible by the generosity of the Max Planck Institute for Complex Systems in Dresden. This is of course part of the purpose of the Institute but the organizers are nevertheless very grateful for the support which includes not only financial but also the quiet and stimulating environment, the well-functioning infrastructure and the efficient secretarial assistance.