Almost any of the great textbooks available on scattering theory continues to explain how a collision experiment measures scattering cross sections for different events, and relates the relevant S-matrix elements, or the scattering amplitudes (onshell T-matrix), to those cross sections. We highly recommend Taylor’s book in this respect. In this volume and the volume that will follow, however, our motivation does not lie in (although discussions can be extended to) the theoretical description of collision experiments. We are mostly interested in applications of scattering theory in few-body physics and effective interactions in few- and many-body physics. Therefore, we consider a method that is having huge success in the theoretical and numerical description of collisions in nuclear physics and quantum chromodynamics, as well as ultracold atomic and condensed matter physics recently. The method allows for an estimation of low-energy scattering parameters and binding energies from exact diagonalisation, in the low-energy sector, of the system’s Hamiltonian, and is originally due to Lüscher [2]. Lacking another term for it, we have decided to simply label this and related methods ‘modern scattering theory’.
Almost any of the great textbooks available on scattering theory continues to explain how a collision experiment measures scattering cross sections for different events, and relates the relevant S-matrix elements, or the scattering amplitudes (onshell T-matrix), to those cross sections. We highly recommend Taylor’s book in this respect. In this volume and the volume that will follow, however, our motivation does not lie in (although discussions can be extended to) the theoretical description of collision experiments. We are mostly interested in applications of scattering theory in few-body physics and effective interactions in few- and many-body physics. Therefore, we consider a method that is having huge success in the theoretical and numerical description of collisions in nuclear physics and quantum chromodynamics, as well as ultracold atomic and condensed matter physics recently. The method allows for an estimation of low-energy scattering parameters and binding energies from exact diagonalisation, in the low-energy sector, of the system’s Hamiltonian, and is originally due to Lüscher [2]. Lacking another term for it, we have decided to simply label this and related methods ‘modern scattering theory’.
This book presents a detailed account of the theory and methods to tackle systems of strongly interacting particles from a bottom-up approach, which has been largely developed in the past decade by the authors and other experts in the field. This begins with a full characterisation of strongly interacting few-particle systems, which can be dealt with accurately using a variety of analytical and numerical techniques. These non-perturbative solutions can be used to gain qualitative and quantitative insight into more complex problems, especially the many-body problem. The book gives a detailed overview of the relevant and current research literature in the field, and is a valuable tool for researchers and graduate students.Part of IOP Series in Quantum Technology. Key features • Many worked examples of representative quantum systems, together with their physical interpretations and the main consequences of their solutions • Set of problems at the end of each chapter, not meant to complement the theory, but to give the reader dexterity in using the chapter’s methodologies • Timely discussion of a recently developed, and very active field summarised as “From Few- to Many-Body Quantum Physics of Strongly Interacting Particles”, and the physics of interacting quantum systems in inhomogeneous media • First, coherent, detailed monograph on the theory and methods of the field • Presents a rigorous account of the modern approaches to low-energy collisions and their use in few- and many-body physics, which have not appeared in book format • The book is relevant to a wide range of researchers and advanced students, from atomic and condensed matter physics, to photonics and nuclear physics • Written by pioneers and true experts in the field
Scattering is one of the most powerful methods used to study the structure of matter, and many of the most important breakthroughs in physics have been made by means of scattering. Nearly a century has passed since the first investigations in this field, and the work undertaken since then has resulted in a rich literature encompassing both experimental and theoretical results. In scattering, one customarily studies collisions among nuclear, sub-nuclear, atomic or molecular particles, and as these are intrinsically quantum systems, it is logical that quantum mechanics is used as the basis for modern scattering theory. In Principles of Quantum Scattering Theory, the author judiciously combines physical intuition and mathematical rigour to present various selected principles of quantum scattering theory. As always in physics, experiment should be used to ultimately validate physical and mathematical modelling, and the author presents a number of exemplary illustrations, comparing theoretical and experimental cross sections in a selection of major inelastic ion-atom collisions at high non-relativistic energies. Quantum scattering theory, one of the most beautiful theories in physics, is also very rich in mathematics. Principles of Quantum Scattering Theory is intended primarily for graduate physics students, but also for non-specialist physicists for whom the clarity of exposition should aid comprehension of these mathematical complexities.
The chapter begins with a brief survey of concepts and techniques of experimental condensed matter physics. It will be shown how correlation functions provide a bridge between concrete experimental data and the theoretical formalism developed in previous chapters. Specifically we discuss – an example of outstanding practical importance – how the response of many-body systems to various types of electromagnetic perturbation can be described in terms of correlation functions and how these functions can be computed by field theoretical means. In the previous chapters we have introduced important elements of the theory of quantum many-body systems. Perhaps most importantly, we have learned how to map the basic microscopic representations of many-body systems onto effective low-energy models. However, to actually test the power of these theories, we need to understand how they can be related to experiment. This will be the principal subject of the present chapter. Modern condensed matter physics benefits from a plethora of sophisticated and highly refined techniques of experimental analysis including the following: electric and thermal transport; neutron, electron, Raman, and X-ray scattering; calorimetric measurements; induction experiments; and many more (for a short glossary of prominent experimental techniques, see Section 7.1.2 below). While a comprehensive discussion of modern experimental condensed matter would reach well beyond the scope of the present text, it is certainly profitable to attempt an identification of some structures common to most experimental work in many-body physics.
Over the last two decades cold atoms have emerged as a most useful platform for exploring quantum science and quantum technology. Cooling, trapping and manipulating atomic systems require understanding of low energy collisions physics. The purpose of this book is to bridge the gap between graduate teaching in scattering theory, particularly atomic scattering, and the emergent fields of cold atoms and cold molecules. Although this book presents basics of collisions physics as applicable to different branches of physics and chemistry, it is written with a particular emphasis on the physics of low energy quantum collisions and its applications to cold atoms. Key features • Pedagogic description of the topics will make this book suitable for graduate students taking courses on quantum scattering theory and cold atomic physics. • Each chapter will have exercises and worked examples. • Emphasises applications of theory to current research topics in several inter-related areas. • Incorporates numerical techniques. • Self-contained, with appendices summarising related topics needed by students.
The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities and theoretical approaches are opening windows into the richness of many-body phenomena in QCD. A common theme is the use of effective field theory (EFT) methods, which exploit the separation of scales in physical systems. At low energies, effective field theory can explain how existing phenomenology emerges from QCD and how to refine it systematically. More generally, the application of EFT methods to many-body problems promises insight into the analytic structure of observables, the identification of new expansion parameters, and a consistent organization of many-body corrections, with reliable error estimates. 1
The chapter begins with a brief survey of concepts and techniques of experimental condensed matter physics. It will be shown how correlation functions provide a bridge between concrete experimental data and the theoretical formalism developed in previous chapters. Specifically we will discuss – an example of outstanding practical importance – how the response of many-body systems to various types of electromagnetic perturbations can be described in terms of correlation functions and how these functions can be computed by field theoretical means. In the previous chapters we have introduced important elements of the theory of quantum many-body systems. Perhaps most importantly, we have learned how to map the basic microscopic representations of many-body systems onto effective low-energy models. However, to actually test the power of these theories, we need to understand how they can be related to experiment. This will be the principal subject of the present chapter. Modern condensed matter physics benefits from a plethora of sophisticated and highly refined techniques of experimental analysis including the following: electric and thermal transport; neutron, electron, Raman, and X-ray scattering; calorimetric measurements; induction experiments; and many more (for a short glossary of prominent experimental techniques, see Section 7.1.2 below). While a comprehensive discussion of modern experimental condensed matter would reach well beyond the scope of the present text, it is certainly profitable to attempt an identification of some structures common to most experimental work in many-body physics.