This book presents a comprehensive account of Bose-Einstein Condensation (BEC), a fundamental phenomenon in quantum physics that reveals the collective behavior of bosonic systems at ultracold temperatures. Bridging theoretical models with experimental developments and applied perspectives, the book is structured to guide readers from foundational principles to advanced topics in the physics of quantum fluids. It is intended for researchers and graduate students in theoretical physics, particularly in condensed matter and ultracold atomic systems.

Topics include the distinction between quantum gases and liquids, the role of the chemical potential in ultracold systems, and the historical and theoretical development of interacting Bose gases since the early work of Bogoliubov. The limitations of Bogoliubov theory-particularly its applicability to weakly interacting systems and neglect of finite-temperature effects-are discussed, along with recent advances such as the Lee-Huang-Yang (LHY) correction and the emergence of quantum droplets in two-component Bose mixtures.

The book introduces field-theoretical methods for many-body systems, covering spontaneous symmetry breaking, Green functions, Matsubara formalism, and path integrals. A central focus is the application of Optimized Perturbation Theory (OPT), also known as the variational Gaussian approximation or linear delta expansion, to atomic BECs and quantum magnets (triplons). Theoretical developments are complemented by a brief overview of experimental methods.

Autorentext

Abdulla Rakhimov earned his M.Sc. in 1977 from Tashkent State University and completed his Ph.D. in Physics and Mathematics at the Joint Institute for Nuclear Research (JINR), Dubna, in 1983. He was awarded the Doctor of Sciences degree in 2005 by the National University of Uzbekistan. Prof. Rakhimov is currently Head Researcher of the Theoretical Physics Department at the Institute of Nuclear Physics. His research spans nonperturbative methods in quantum field theory, phase transitions in quantum magnets, superconductivity, Bose-Einstein condensates, and the application of path integral techniques in condensed matter physics. He has co-authored over 60 publications in peer-reviewed journals and has collaborated with numerous international institutions. Notable recent works include publications in Physical Review A, Journal of Physics: Condensed Matter, and Annals of Physics.

Shukhrat Mardonov is Head of the Research Department at New Uzbekistan University. In 2012, he received a Ph.D. scholarship through the European Union-funded Erasmus Mundus program and completed his doctorate at the University of the Basque Country, Bilbao, in 2015. His research interests focus on the thermodynamics and dynamics of Bose-Einstein condensates, including triplon condensation and the optical properties of quantum gases. Prof. Mardonov has authored several peer-reviewed articles in journals indexed by Scopus and Web of Science, and contributed a chapter titled "Effects of Anomalous Velocity in Spin-Orbit Coupled Systems" to Spin Orbitronics and Topological Properties of Nanostructures (World Scientific Publishing, Lecture Notes of the 12th International School on Theoretical Physics).