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Momentum Space Techniques in Few-Body Physics: Bound and Continuum

Marcelo Takeshi Yamashita

Published Oct 25, 2017• 1 citation
OpenAlex

Abstract

These notes were written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop Critical Stability of Quantum Few-Body Systems. These lectures are primarily dedicated to the students and represent a very idiosyncratic vision of the author, mainly in the last part of the text related to applications. These notes are only a tentative to show a technique, among many others, to solve problems in a very rich area of the contemporary physics - the Few-Body Physics - many times unknown by a considerable part of the students.

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These notes were written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop Critical Stability of Quantum Few-Body Systems. These lectures are primarily dedicated to the students and represent a very idiosyncratic vision of the author, mainly in the last part of the text related to applications. These notes are only a tentative to show a technique, among many others, to solve problems in a very rich area of the contemporary physics - the Few-Body Physics - many times unknown by a considerable part of the students.
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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
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed.