An introduction to ultracold atoms with analytical and numerical methods /

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An introduction to ultracold atoms with analytical and numerical methods /

Muruganandam, Paulsamy, - Personal Name; Institute of Physics (Great Britain), - Personal Name; sRadha, Ramaswamy, - Personal Name;

"Version: 20251101"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. History of Bose-Einstein condensates -- 1.2. Bose-Einstein condensation : an experimental and theoretical perspective -- 1.3. Mean field description and Gross-Pitaevskii equation -- 1.4. Fermionic condensates -- 1.5. Beyond mean-field description -- 1.6. Outline2. Analytical methods -- 2.1 Inverse scattering transform -- 2.2. Gauge transformation approach -- 2.3. Darboux transformation approach -- 2.4. Hirota (direct) method -- 2.5. Modified gauge transformation method -- 2.6. Derivation of soliton solutions--illustration -- 2.7. Defocussing Manakov model -- 2.8. Summary and future challenges -- 2.9. Problems3. Numerical techniques -- 3.1. The Gross-Pitaevskii (GP) equation -- 3.2. Split-step Crank-Nicolson method -- 3.3. Split-step Fourier transform method -- 3.4. Newton conjugate-gradient methods -- 3.5. Bayesian optimization of BECs--data-driven approach -- 3.6. Background -- 3.7. Methods -- 3.8. Experiments -- 3.9. Summary and future challenges -- 3.10. Problems4. Bose-Einstein condensates and optical solitons -- 4.1. Coupled nonlinear Schr?odinger equations -- 4.2. Coupled nonlinear Schr?odinger equations (the Manakov model) : new signatures -- 4.3. Lax pair and bright solitons -- 4.4. Coherently coupled nonlinear Schr?odinger equations -- 4.5. Four-wave mixing induced manipulation of light in coupled nonlinear Schr?odinger equations -- 4.6. Propagation of light through matter and electromagnetically induced transparency -- 4.7. Summary and future challenges5. Dynamics of scalar Bose-Einstein condensates with short-range interactions -- 5.1. Quasi-one-dimensional Bose-Einstein condensates in a time-independent harmonic trap -- 5.2. Impact of transient trap on Bose-Einstein condensates -- 5.3. Matter-wave interference pattern in the collision of solitons -- 5.4. Bose-Einstein condensates with attractive and repulsive three-body interactions -- 5.5. Summary and future challenges6. Vectorial condensates -- 6.1. Vector Bose-Einstein condensates and Feshbach resonance management -- 6.2. Enhancement of lifetime and collisional dynamics of vector BECs -- 6.3. Impact of temporal Rabi coupling -- 6.4. Spatially coupled Bose-Einstein condensates -- 6.5. Taming of rogue waves in vector BECs -- 6.6. Summary and future challenges7. Spin-orbit-coupled Bose-Einstein condensates -- 7.1. Synthetic spin-orbit and Rabi coupling in Bose-Einstein condensates -- 7.2. Model and Lax pair -- 7.3. Darboux transformation -- 7.4. Rogue waves, breathers, bright and dark solitons -- 7.5. Numerical methods -- 7.6. Plane wave and stripe patterns -- 7.7. Dynamics of SO-coupled BECs -- 7.8. Summary and future challenges -- 7.9. Problems8. Bose-Einstein condensates with long-range interactions -- 8.1. Dipolar Bose-Einstein condensates -- 8.2. Mean-field dipolar Gross-Pitaevskii (GP) equation -- 8.3. Split-step Crank-Nicolson method for dipolar Gross-Pitaevskii equations -- 8.4. Ground state properties of dipolar BECs -- 8.5. Summary and future challenges -- 8.6. Problems9. Collisionally inhomogenous Bose-Einstein condensates -- 9.1. Model and evolution equation -- 9.2. Faraday and resonant waves in scalar Bose-Einstein condensates -- 9.3. Faraday and resonant waves in binary condensates -- 9.4. Stable multiple vortices in collisionally inhomogeneous attractive Bose-Einstein condensates -- 9.5. Solitons under spatially localized cubic-quintic-septimal nonlinearities10. Quantum vortices in Bose-Einstein condensates -- 10.1. Single-vortex dynamics -- 10.2. Vortex lattices in BECs -- 10.3. Vortices in Thomas-Fermi regime -- 10.4. Vortices in lowest Landau level -- 10.5. Phase transitions to highly correlated states -- 10.6. Vortex stability and Bogoliubov equations -- 10.7. Vortices in dipolar BECs -- 10.8. Vortex formation via merging BECs -- 10.9. Vortex dynamics in dipolar BECs -- 10.10. Summary and future challenges11. Nascent outlook of exciton-polariton condensates -- 11.1. Theoretical model -- 11.2. Variational approach -- 11.3. Collisions of bright solitons with an unexcited impurity -- 11.4. Stability window of trapless polariton Bose-Einstein condensates -- 11.5. Summary and future challenges12. Roadmap ahead -- 12.1. Supersolids -- 12.2. Quantum droplets -- 12.3. Quantum turbulence in BECs -- 12.4. ProblemsAppendix A. Note on computational tools for the Gross-Pitaevskii equation -- Appendix B. Raman-induced spin-orbit coupling in a spin-1 Bose-Einstein condensate -- Appendix C. Expression for the dipole-dipole interaction potential in the Fourier domain.Full-text restricted to subscribers or individual document purchasers.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.Graduate level students pursuing work with ultracold atoms/BECs/ nonlinear optics/nonlinear dynamics.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Paulsamy Muruganandam is a professor and head of the department of physics at Bharathidasan University. With 18 years teaching experience and over 25 years of research experience, his areas of interest include ultracold systems; matter waves; computational physics; nonlinear dynamics; complex systems; machine learning. Ramasamy Radha is currently an associate professor and department head of the Centre for Nonlinear Science at the Government collect for Women, India. Her areas of interest include solitons and integrability in higher dimensions, magnetic spin systems, nonlinear optics and Bose-Einstein condensates.Title from PDF title page (viewed on December 1, 2025).

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Series Title: -
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Publisher: : .,
Collation: 1 online resource (various pagings) :illustrations (some color).
Language: English
ISBN/ISSN: 9780750354479
Classification: 530.4/2
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Edition: -
Subject(s): Optical physics.
SCIENCE / Physics / Optics & Light.
Quantum theory
Nonlinear theories.
Bose-Einstein condensation.
Bose-Einstein condensation
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Statement of Responsibility: Paulsamy Muruganandam, Ramaswamy Radha.

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