Preface

The term “finite Fermi systems” usually refers to systems where the fermionic nature of the constituents is of dominating importance but the finite spatial extent also cannot be ignored. Historically the prominent examples were atoms, molecules, and nuclei. These should be seen in contrast to solid-state systems, where an infinite extent is usually a good approximation. Recently, new and different types of finite Fermi systems have become important, most noticeably metallic clusters, quantum dots, fermion traps, and compact stars. The theoretical description of finite Fermi systems has a long tradition and developed over decades from most simple models to highly elaborate methods of manybody theory. In fact, finite Fermi systems are the most demanding ground for theory as one often does not have any symmetry to simplify classification and as a possibly large but always finite particle number requires to take into account all particles. In spite of the practical complexity, most methods rely on simple and basic schemes which can be well understood in simple test cases. We therefore felt it a timely undertaking to offer a comprehensive view of the underlying theoretical ideas and techniques used for the description of such systems across physical disciplines. The book demonstrates how theoretical can be successively refined from the Fermi gas via external potential and mean-field models to various techniques for dealing with residual interactions, while following the universality of such concepts like shells and magic numbers across the application fields. We assume a familiarity with electrodynamic and quantum theory as presented in the usual introductory theory courses. Many-body techniques are for the most part developed in the book itself, although some prior acquaintance might be useful. They are, however, kept at a relatively low level throughout the book, staying within the confines of elementary second quantization without any resort to field theoretic techniques. The accompanying software allows applying some of the models in simplified scenarios that are still sophisticated enough to contain all the essential qualitative ingredients, on which more refined models may be built even by the creative reader. The authors would like to acknowledge the numerous fruitful discussions with several colleagues on teaching topics related to this book. One of us (E. Suraud) would make a special mention to P.M. Dinh and P. Quentin who were especially