Stationary And Time Dependent Gross Pitaevskii Equations

Download or read book Stationary and Time Dependent Gross-Pitaevskii Equations written by Wolfgang Pauli Institute. Thematic Program and published by American Mathematical Soc.. This book was released on 2008 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume looks at the Gross-Pitaevskii equation, an example of a defocusing nonlinear Schrodinger equation, which is a model for phenomena such as the Bose-Einstein condensation of ultra cold atomic gases, the superfluidity of Helium II, and the 'dark solitons' of nonlinear optics.

Download or read book Hamiltonian Partial Differential Equations and Applications written by Philippe Guyenne and published by Springer. This book was released on 2015-09-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Download or read book Selforganization in Complex Systems: The Past, Present, and Future of Synergetics written by Günter Wunner and published by Springer. This book was released on 2015-12-26 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains talks and poster presentations from the International Symposium "Self-Organization in Complex Systems: The Past, Present, and Future of Synergetics", which took place at Hanse-Wissenschaftskolleg, an Institute of Advanced Studies, in Delmenhorst, Germany, during the period November 13 - 16, 2012. The Symposium was organized in honour of Hermann Haken, who celebrated his 85th birthday in 2012. With his fundamental theory of Synergetics he had laid the mathematical-physical basis for describing and analyzing self-organization processes in a diversity of fields of research. The quest for common and universal principles of self-organization in complex systems was clearly covered by the wide range of interdisciplinary topics reported during the Symposium. These extended from complexity in classical systems and quantum systems over self-organisation in neuroscience even to the physics of finance. Moreover, by combining a historical view with a present status report the Symposium conveyed an impression of the allure and potency of this branch of research as well as its applicability in the future.

Download or read book Nonlinear Dispersive Equations written by Christian Klein and published by Springer Nature. This book was released on 2021 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.

Download or read book Superfluid States of Matter written by Boris V. Svistunov and published by CRC Press. This book was released on 2015-04-15 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the State of the Art in Superfluidity and SuperconductivitySuperfluid States of Matter addresses the phenomenon of superfluidity/superconductivity through an emergent, topologically protected constant of motion and covers topics developed over the past 20 years. The approach is based on the idea of separating universal classical-field superf

Download or read book Localization in Periodic Potentials written by Dmitry E. Pelinovsky and published by Cambridge University Press. This book was released on 2011-10-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book describes modern methods in the analysis of reduced models of Bose–Einstein condensation in periodic lattices. Aimed at researchers and graduate students working in applied mathematics and physical sciences where nonlinear waves arise, its unique focus is on localized nonlinear waves in periodic potentials and lattices.

Download or read book Quantum World Of Ultra-cold Atoms And Light, The - Book Iii: Ultra-cold Atoms written by Crispin W Gardiner and published by World Scientific. This book was released on 2017-09-07 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This century has seen the development of technologies for manipulating and controlling matter and light at the level of individual photons and atoms, a realm in which physics is fully quantum-mechanical. The dominant experimental technology is the laser, and the theoretical paradigm is quantum optics.The Quantum World of Ultra-Cold Atoms and Light is a trilogy, which presents the quantum optics way of thinking and its applications to quantum devices. This book — 'Ultra-Cold Atoms' — provides a theoretical treatment of ultra-cold Bosons and Fermions and their interactions with electromagnetic fields in a form consistent with the first two books in the trilogy.The central concept is the quantum stochastic paradigm, formulated for cold collision physics. For Bosons, this yields a suite of techniques; versions of the stochastic Gross-Pitaevskii equation, using which a wide range of dynamic and thermal properties are formulated.The eBook editions of the 'Quantum World Trilogy' feature an extensive system of hyperlinks for ease of cross reference within the books, as well as links to the other books in the trilogy. In the section Viewing the eBooks we explain how these links work, and give some advice on appropriate pdf viewer applications.