An Introduction To Lieb S Simplified Approach To The Bose Gas
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An Introduction To Lieb S Simplified Approach To The Bose Gas
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Author : Ian Jauslin
language : en
Publisher: Springer Nature
Release Date : 2025-01-30
An Introduction To Lieb S Simplified Approach To The Bose Gas written by Ian Jauslin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Science categories.
This book explores Lieb's Simplified approach to the ground state of systems of interacting bosons. While extensive research has delved into the behavior of interacting bosons, persistent challenges, such as proving Bose-Einstein condensation, remain. Introduced by Lieb in 1963, the Simplified approach has been the object of renewed attention in recent years, revealing surprising and promising results. Notably, this approach provides ground state energy predictions that agree with many-body systems asymptotically at both low and high densities. It further predicts a condensate fraction and correlation function that agree with Bogolyubov theory at low densities, and numerical predictions match quantum Monte Carlo simulations across all densities. This suggests that Lieb's Simplified approach could serve as a potent tool for reimagining the study of interacting bosons. The book defines Lieb's Simplified approach, discusses its predictions, and presents known analytical and numerical results. It is designed for advanced students and young researchers working in the fields of mathematical physics, quantum many-body physics and Bose-Einstein condensates.
Condensed Matter Physics And Exactly Soluble Models
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Author : Elliott H. Lieb
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Condensed Matter Physics And Exactly Soluble Models written by Elliott H. Lieb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
The Mathematics Of The Bose Gas And Its Condensation
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Author : Elliott H. Lieb
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
The Mathematics Of The Bose Gas And Its Condensation written by Elliott H. Lieb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-17 with Science categories.
This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.
Bose Einstein Condensation In Dilute Gases
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Author : C. J. Pethick
language : en
Publisher: Cambridge University Press
Release Date : 2002
Bose Einstein Condensation In Dilute Gases written by C. J. Pethick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
In 1925 Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose-Einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates has become one of the most active areas in contemporary physics. The study of Bose-Einstein condensates in dilute gases encompasses a number of different subfields of physics, including atomic, condensed matter, and nuclear physics. The authors of this graduate-level textbook explain this exciting new subject in terms of basic physical principles, without assuming detailed knowledge of any of these subfields. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problem sets are also included in each chapter.
Essays In Theoretical Physics
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Author : W. E. Parry
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Essays In Theoretical Physics written by W. E. Parry and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Essays in Theoretical Physics: In Honour of Dirk ter Haar is devoted to Dirk ter Haar, detailing the breadth of Dirk's interest in physics. The book contains 15 chapters, with some chapters elucidating stellar dynamics with non-classical integrals; a mean-field treatment of charge density waves in a strong magnetic field; electrodynamics of two-dimensional (surface) superconductors; and the Bethe Ansatz and exact solutions of the Kondo and related magnetic impurity models. Other chapters focus on probing the interiors of neutron stars; macroscopic quantum tunneling; unitary transformation methods in intense fields atomic physics; stochastic parameters in quantum mechanical systems; and correlation effects in atomic diffusion. The book also describes the densely packed magnetic insulator glasses, nuclei in dense matter, solar neutrinos, comets, cosmic rays, the Gibbs paradox, and wave packets.
Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1963
Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Electrical engineering categories.
Correlations In Low Dimensional Quantum Gases
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Author : Guillaume Lang
language : en
Publisher: Springer
Release Date : 2018-12-29
Correlations In Low Dimensional Quantum Gases written by Guillaume Lang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-29 with Science categories.
The book addresses several aspects of thermodynamics and correlations in the strongly-interacting regime of one-dimensional bosons, a topic at the forefront of current theoretical and experimental studies. Strongly correlated systems of one-dimensional bosons have a long history of theoretical study. Their experimental realisation in ultracold atom experiments is the subject of current research, which took off in the early 2000s. Yet these experiments raise new theoretical questions, just begging to be answered. Correlation functions are readily available for experimental measurements. In this book, they are tackled by means of sophisticated theoretical methods developed in condensed matter physics and mathematical physics, such as bosonization, the Bethe Ansatz and conformal field theory. Readers are introduced to these techniques, which are subsequently used to investigate many-body static and dynamical correlation functions.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1966
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Nuclear energy categories.
The Bethe Wavefunction
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Author : Michel Gaudin
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-06
The Bethe Wavefunction written by Michel Gaudin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-06 with Science categories.
Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers in physics. It presents a mixture of mathematics interspersed with powerful physical intuition, retaining the author's unmistakably honest tone. The book begins with the Heisenberg spin chain, starting from the coordinate Bethe Ansatz and culminating in a discussion of its thermodynamic properties. Delta-interacting bosons (the Lieb-Liniger model) are then explored, and extended to exactly solvable models associated to a reflection group. After discussing the continuum limit of spin chains, the book covers six- and eight-vertex models in extensive detail, from their lattice definition to their thermodynamics. Later chapters examine advanced topics such as multi-component delta-interacting systems, Gaudin magnets and the Toda chain.