Simple Models of Many-Fermion Systems

In this user-friendly guide to the physics of many-particle systems, the material is developed along simple and generic models which illuminate the basic mechanisms behind each approach and which apply to a variety of systems in physics and chemistry.

The term nite Fermi systems usually refers to systems where the fermionic nature of the constituents is of dominating importance but the nite 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 in nite extent is usually a good approximation. Recently, new and different types of nite Fermi systems have become important, most noticeably metallic clusters, quantum dots, fermion traps, and compact stars. The theoretical description of nite Fermi systems has a long tradition and dev- oped over decades from most simple models to highly elaborate methods of ma- body theory. In fact, nite Fermi systems are the most demanding ground for theory as one often does not have any symmetry to simplify classi cation and as a possibly large but always nite 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 s- tems across physical disciplines. The book demonstrates how theoretical can be successively re ned from the Fermi gas via external potential and mean- eld m- els to various techniques for dealing with residual interactions, while following the universality of such concepts like shells and magic numbers across the application elds.

First overview addressing such a cross-disciplinary topic Material for a one semester course Working tool with practical examples and applications Includes supplementary material: sn.pub/extras

Autorentext
All three authors are teaching since many years at various university levels. They also have experience in teaching in international summer schools and they have already written several textbooks in nuclear and cluster physics.

Klappentext

The purpose of this book is to provide a pedestrians route to the physics of many-particle systems. The material is developed along simple and generic models which allow to illuminate the basic mechanisms beyond each approach and which apply to broad variety of systems in different areas of physics and chemistry. The book is sorted in steps of slowly increasing complexity of the models. Complementing numerical tools help to carry on where analytical methods reach their limits. They provide at the same time a useful training for the typical numerical methods in many-body physics.

In order to confine the huge field, we shall focus the discussions on finite systems wherefrom we take the examples of applications. This covers nuclei, atoms, molecules and clusters. The idea of this book is to concentrate first on the generic, robust and simple, approaches and show how they apply to several domains across the specific disciplines. On the other hand, we aim to establish contact with actual research by carrying forth some examples up to realistic applications, attacked with help of a set of simple and still general codes provided at an online repository linked to the book. This latter aspect emphasizes our intention to guide the reader in practizing the tools presented in the book, both at schematic and realistic levels.

Inhalt
The Variety of Finite Fermion Systems and Their Basic Properties.- The Fermi-Gas Model.- Particles in an External Field.- Approaches Based on Model Spaces.- HartreeFock.- Density Functional Theory.- Quasispin Models.- Excitation Spectra.- Coherent Two-Body Correlations.- Conclusions.