Strongly Interacting Quantum Systems, Volume 1
Description
When systems of particles interact strongly, their few- and many-body properties can exhibit some highly non-trivial phenomenology that is absent in their weakly-coupled and non-interacting counterparts. Remarkable effects range from the Efimov effect, to the transition from molecule to "dressed" single particle (polaron) when an impurity is embedded in a Fermi gas. The description of strong interactions is very challenging since perturbation theory, so successful in describing many fundamental phenomena (e.g. in Quantum Electrodynamics), is of no use. Here is where few-body physics can be of great aid, since many few-body problems can be accurately solved and, moreover, can be cleverly related to the many-body problem in a large variety of problems.
This book presents a detailed account of the theory and methods to tackle the aforementioned systems 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.
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Manuel Valiente did his PhD on the physics of few interacting quantum particles in optical lattices, graduating from the Humboldt-Universitaet zu Berlin (Germany) in 2010, with research done as a Marie-Curie Early Stage Researcher at the Institute for Electronic Structure & Laser - FoRTH in Heraklion, Crete. He then moved to Aarhus University as a postdoctoral researcher where he started to work on using few-body concepts to describe non-perturbative effects in the many-body problem. After that, he spent six years at Heriot-Watt University before joining the Faculty at the Institute of Advanced Study, Tsinghua University as an Associate Member. His current research interests revolve around the description of strong interactions and universality in the few- and many-body problems in ultracold atomic and condensed matter physics, including topologically non-trivial systems.
After graduate work in theoretical nuclear physics and astrophysics, Dr. Zinner moved into cold atomic gases and condensed matter physics, securing individual grants to be able to pursue his own ideas and venture into new fields with great success. Dr. Zinner has contributed high-quality papers in all fields he has worked in thus far. Early prestigious career grants (The Elite Research Prize grant 2011 and Sapere Aude Starting Grant 2013) enabled Dr. Zinner to build a group early on in his career and strengthen international collaborations to become an independent research group leader and authority in the field of few-body physics, as well as its applications in various platforms related to quantum technology. Later on, Dr. Zinner was the recipient of a three-year fellowship at Aarhus Institute of Advanced Studies (2019-2021), a prestigious interdisciplinary research institute, as well as a Carlsberg Foundation Distinguished Associate Professor (2017-2020), and in 2022 Dr. Zinner received one of the coveted Pathfinder grants from the European Innovation Council. With more than 250 papers, among them three review papers, Dr. Zinner has an impressive publication record across several fields.
Content
Preface
Acknowledgements
Author biographies
1 Fundamentals of quantum mechanics and scattering theory
2 Modern scattering theory
3 Effective field theory of interactions and renormalization
4 Atoms, electrons and photons in structured media
5 Dimensional reduction of trapped interacting quantum systems
6 One- and two-body physics
7 Three-body physics
Appendix A: Useful formulae
