Author: Elliott H. Lieb
Publisher: Springer Science & Business Media
ISBN: 3662034360
Category : Science
Languages : en
Pages : 677
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Book Description
The first edition of "The Stability of Matter: From Atoms to Stars" was sold out after a time unusually short for a selecta collection and we thought it ap propriate not just to make a reprinting but to include eight new contributionso They demonstrate that this field is still lively and keeps revealing unexpected featureso Of course, we restricted ourselves to developments in which Elliott Lieb participated and thus the heroic struggle in Thomas-Fermi theory where 7 3 5 3 the accuracy has been pushed from Z 1 to Z 1 is not includedo A rich landscape opened up after Jakob Yngvason's observation that atoms in magnetic fields also are described in suitable limits by a Thomas-Fermi-type theoryo Together with Elliott Lieb and Jan Philip Solovej it was eventually worked out that one has to distinguish 5 regionso If one takes as a dimensionless measure of the magnetic field strength B the ratio Larmor radius/Bohr radius one can compare it with N "' Z and for each of the domains 4 3 (i) B « N 1 , 4 3 (ii) B "' N 1 , 4 3 3 (iii) N 1« B « N , 3 (iv) B "' N , 3 (v) B » N a different version ofmagnetic Thomas-Fermi theory becomes exact in the limit N --+ ooo In two dimensions and a confining potential ("quantum dots") the situation is somewhat simpler, one has to distinguish only (i) B « N, (ii) B "'N,
Author: Elliott H. Lieb
Publisher: Springer Science & Business Media
ISBN: 3764373377
Category : Science
Languages : en
Pages : 204
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Book Description
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.
Author: Lizhen Ji
Publisher: American Mathematical Soc.
ISBN: 0821875876
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
Author: C. J. Pethick
Publisher: Cambridge University Press
ISBN: 9780521665803
Category : Science
Languages : en
Pages : 420
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Book Description
Problems after each chapter
Author: Giuseppe Gaeta
Publisher: Springer Nature
ISBN: 1071626213
Category : Science
Languages : en
Pages : 601
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Book Description
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
Author: Michele Correggi
Publisher: Springer Nature
ISBN: 9819958849
Category : Science
Languages : en
Pages : 371
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Book Description
This book is the second volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to quantum field theory and open quantum systems.
Author: M. Inguscio
Publisher: IOS Press
ISBN: 9780967335551
Category : Atomic gases
Languages : en
Pages : 732
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Book Description
Although first proposed by Einstein in 1924, Bose-Einstein condensation (BEC) in a gas was not achieved until 1995 when, using a combination of laser cooling and trapping, and magnetic trapping and evaporation, it was first observed in rubidium and then in lithium and sodium, cooled down to extremely low temperatures. This book brought together many leaders in both theory and experiment on Bose-Einstein condensation in gases. Their lectures provided a detailed coverage of the experimental techniques for the creation and study of BEC, as well as the theoretical foundation for understanding the properties of this novel system. This volume provides the first systematic review of the field and the many developments that have taken place in the past three years.
Author: Rudi Weikard
Publisher: American Mathematical Soc.
ISBN: 0821821571
Category : Mathematics
Languages : en
Pages : 491
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Book Description
This volume contains the proceedings of the 1999 International Conference on Differential Equations and Mathematical Physics. The contributions selected for this volume represent some of the most important presentations by scholars from around the world on developments in this area of research. The papers cover topics in the general area of linear and nonlinear differential equations and their relation to mathematical physics, such as multiparticle Schrödinger operators, stability of matter, relativity theory, fluid dynamics, spectral and scattering theory including inverse problems. Titles in this series are co-published with International Press, Cambridge, MA.
Author: Società italiana di fisica
Publisher: IOS Press
ISBN: 1614992258
Category : Science
Languages : en
Pages : 664
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Book Description
Although first proposed by Einstein in 1924, Bose-Einstein condensation (BEC) in a gas was not achieved until 1995 when, using a combination of laser cooling and trapping, and magnetic trapping and evaporation, it was first observed in rubidium and then in lithium and sodium, cooled down to extremely low temperatures. This book brought together many leaders in both theory and experiment on Bose-Einstein condensation in gases. Their lectures provided a detailed coverage of the experimental techniques for the creation and study of BEC, as well as the theoretical foundation for understanding the properties of this novel system. This volume provides the first systematic review of the field and the many developments that have taken place in the past three years.
Author: Jean-claude Zambrini
Publisher: World Scientific
ISBN: 9814480762
Category : Science
Languages : en
Pages : 718
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Book Description
In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.
