The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers.This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose–Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers.This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose–Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
The 1995 observation of Bose–Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems. This self-contained volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose–Einstein condensates, degenerate Fermi gases, and the more recently realised exciton–polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of editorial notes. Both graduate students and established researchers wishing to understand the state of the art will greatly benefit from this comprehensive and up-to-date review of non-equilibrium and finite temperature techniques in the exciting and expanding field of quantum gases and liquids.
This book offers a detailed introduction to Bose-Einstein condensates (BECs) and nonlinear quantum systems, tailored for advanced undergraduates and researchers. It bridges foundational concepts with modern developments in quantum condensed matter. Starting with the history and experimental milestones of BECs, it explores theoretical models including mean-field and beyond-mean-field approaches for both scalar and vectorial condensates. Analytical techniques such as inverse scattering and soliton theory are covered alongside numerical methods for solving the Gross-Pitaevskii equation. Applications span optical solitons, quantum vortices, and exciton-polariton physics. Each topic is supported by examples, problem sets, and computational tools, equipping readers with both theoretical insight and practical skills to engage with cutting-edge research areas like quantum turbulence and supersolids. Part of IOP Series in Advances in Optics, Photonics and Optoelectronics. Key features • Introduces the subject at the very basic level. • Includes the analytical and theoretical methods. • Contains numerical methods. • Provides worked examples, end-of-chapter summaries, and homework problems.
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. This article offers a short survey on mathematical models and theories as well as numerical methods for BEC based on the mean field theory. We start with the Gross-Pitaevskii equation (GPE) in three dimensions (3D) for modeling one-component BEC of the weakly interacting bosons, scale it to obtain a three-parameter model and show how to reduce it to two dimensions (2D) and one dimension (1D) GPEs in certain limiting regimes. Mathematical theories and numerical methods for ground states and dynamics of BEC are provided. Extensions to GPE with an angular momentum rotation term for a rotating BEC, to GPE with long-range anisotropic dipole-dipole interaction for a dipolar BEC and to coupled GPEs for spin-orbit coupled BECs are discussed. Finally, some conclusions are drawn and future research perspectives are discussed.
In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches School of Physics (held for the first time outside Europe in Singapore) brings together experts in both fields. The theme of the school focused on two principal topics: quantum information science and ultracold atomic physics. The topics ranged from Bose-Einstein condensates to degenerate Fermi gases to fundamental concepts in quantum information sciences, including some special topics on quantum Hall effects, quantum phase transition, interactions in quantum fluids, disorder and interference phenomenoma, trapped ions and atoms, and quantum optical devices.
The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.