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Título : Mean Field Models for Spin Glasses : Volume I: Basic Examples Tipo de documento: documento electrónico Autores: Michel Talagrand ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, ISSN 0071-1136 num. 54 Número de páginas: XVIII, 485 p Il.: online resource ISBN/ISSN/DL: 978-3-642-15202-3 Idioma : Inglés (eng) Palabras clave: Mathematics Probabilities Physics Condensed matter Probability Theory and Stochastic Processes Mathematical Methods in Matter Clasificación: 51 Matemáticas Resumen: This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them Nota de contenido: Introduction -- 1. The Sherrington-Kirkpatrick Model -- 2. The Perceptron Model -- 3. The Shcherbina and Tirozzi Model -- 4. The Hopfield Model -- 5. The V-statistics Model -- 6. The Diluted SK Model and the K-Sat Problem -- 7. An Assignment Problem -- A. Appendix: Elements of Probability Theory -- References -- Index -- Glossary En línea: http://dx.doi.org/10.1007/978-3-642-15202-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33378 Mean Field Models for Spin Glasses : Volume I: Basic Examples [documento electrónico] / Michel Talagrand ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - XVIII, 485 p : online resource. - (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, ISSN 0071-1136; 54) .
ISBN : 978-3-642-15202-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Probabilities Physics Condensed matter Probability Theory and Stochastic Processes Mathematical Methods in Matter Clasificación: 51 Matemáticas Resumen: This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them Nota de contenido: Introduction -- 1. The Sherrington-Kirkpatrick Model -- 2. The Perceptron Model -- 3. The Shcherbina and Tirozzi Model -- 4. The Hopfield Model -- 5. The V-statistics Model -- 6. The Diluted SK Model and the K-Sat Problem -- 7. An Assignment Problem -- A. Appendix: Elements of Probability Theory -- References -- Index -- Glossary En línea: http://dx.doi.org/10.1007/978-3-642-15202-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33378 Ejemplares
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Título : Mean Field Models for Spin Glasses : Volume II: Advanced Replica-Symmetry and Low Temperature Tipo de documento: documento electrónico Autores: Michel Talagrand ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, ISSN 0071-1136 num. 55 Número de páginas: XII, 632 p Il.: online resource ISBN/ISSN/DL: 978-3-642-22253-5 Idioma : Inglés (eng) Palabras clave: Mathematics Probabilities Physics Condensed matter Probability Theory and Stochastic Processes Mathematical Methods in Matter Clasificación: 51 Matemáticas Resumen: This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition En línea: http://dx.doi.org/10.1007/978-3-642-22253-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33438 Mean Field Models for Spin Glasses : Volume II: Advanced Replica-Symmetry and Low Temperature [documento electrónico] / Michel Talagrand ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - XII, 632 p : online resource. - (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, ISSN 0071-1136; 55) .
ISBN : 978-3-642-22253-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Probabilities Physics Condensed matter Probability Theory and Stochastic Processes Mathematical Methods in Matter Clasificación: 51 Matemáticas Resumen: This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition En línea: http://dx.doi.org/10.1007/978-3-642-22253-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33438 Ejemplares
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Título : Systèmes multi-échelles : Modélisation et simulation Tipo de documento: documento electrónico Autores: Claude Le Bris ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Mathématiques et Applications, ISSN 1154-483X num. 47 Número de páginas: XII, 214 p. 35 ill Il.: online resource ISBN/ISSN/DL: 978-3-540-37671-2 Idioma : Francés (fre) Palabras clave: Mathematics Partial differential equations Numerical analysis Calculus of variations Probabilities Continuum physics Condensed matter Differential Equations Variations and Optimal Control; Optimization Probability Theory Stochastic Processes Analysis Classical Physics Matter Clasificación: 51 Matemáticas Resumen: Systèmes multi-échelles est une introduction à la problématique des systémes multi-échelles du point de vue du mathématicien appliqué. Il se compose d'une mosaique d'exemples dont le seul lien est d'appartenir à la très grande famille des problèmes issus de la physique au sens large qui présentent pour leur modélisation et leur simulation cette difficulté essentielle de comporter en leur sein des échelles de temps ou d'espace très différentes Nota de contenido: Modèles micro-macro pour les solides -- Techniques d’homogénéisation -- Simulation moléculaire -- Modèles micro-macro pour les fluides -- Cinétique chimique -- Vers une unité des approches En línea: http://dx.doi.org/10.1007/3-540-37671-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35316 Systèmes multi-échelles : Modélisation et simulation [documento electrónico] / Claude Le Bris ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XII, 214 p. 35 ill : online resource. - (Mathématiques et Applications, ISSN 1154-483X; 47) .
ISBN : 978-3-540-37671-2
Idioma : Francés (fre)
Palabras clave: Mathematics Partial differential equations Numerical analysis Calculus of variations Probabilities Continuum physics Condensed matter Differential Equations Variations and Optimal Control; Optimization Probability Theory Stochastic Processes Analysis Classical Physics Matter Clasificación: 51 Matemáticas Resumen: Systèmes multi-échelles est une introduction à la problématique des systémes multi-échelles du point de vue du mathématicien appliqué. Il se compose d'une mosaique d'exemples dont le seul lien est d'appartenir à la très grande famille des problèmes issus de la physique au sens large qui présentent pour leur modélisation et leur simulation cette difficulté essentielle de comporter en leur sein des échelles de temps ou d'espace très différentes Nota de contenido: Modèles micro-macro pour les solides -- Techniques d’homogénéisation -- Simulation moléculaire -- Modèles micro-macro pour les fluides -- Cinétique chimique -- Vers une unité des approches En línea: http://dx.doi.org/10.1007/3-540-37671-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35316 Ejemplares
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Título : The Mathematics of the Bose Gas and its Condensation Tipo de documento: documento electrónico Autores: Elliott H. Lieb ; SpringerLink (Online service) ; Jan Philip Solovej ; Seiringer, Robert ; Jakob Yngvason Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2005 Colección: Oberwolfach Seminars num. 34 Número de páginas: VIII, 208 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7337-5 Idioma : Inglés (eng) Palabras clave: Physics Applied mathematics Engineering Condensed matter Statistical physics Dynamical systems Matter Applications of Mathematics Mathematical Methods in Physics, Systems and Complexity Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: The Dilute Bose Gas in 3D -- The Dilute Bose Gas in 2D -- Generalized Poincaré Inequalities -- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases -- Gross-Pitaevskii Equation for Trapped Bosons -- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases -- One-Dimensional Behavior of Dilute Bose Gases in Traps -- Two-Dimensional Behavior in Disc-Shaped Traps -- The Charged Bose Gas, the One- and Two-Component Cases -- Bose-Einstein Quantum Phase Transition in an Optical Lattice Model En línea: http://dx.doi.org/10.1007/b137508 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35328 The Mathematics of the Bose Gas and its Condensation [documento electrónico] / Elliott H. Lieb ; SpringerLink (Online service) ; Jan Philip Solovej ; Seiringer, Robert ; Jakob Yngvason . - Basel : Birkhäuser Basel, 2005 . - VIII, 208 p : online resource. - (Oberwolfach Seminars; 34) .
ISBN : 978-3-7643-7337-5
Idioma : Inglés (eng)
Palabras clave: Physics Applied mathematics Engineering Condensed matter Statistical physics Dynamical systems Matter Applications of Mathematics Mathematical Methods in Physics, Systems and Complexity Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: The Dilute Bose Gas in 3D -- The Dilute Bose Gas in 2D -- Generalized Poincaré Inequalities -- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases -- Gross-Pitaevskii Equation for Trapped Bosons -- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases -- One-Dimensional Behavior of Dilute Bose Gases in Traps -- Two-Dimensional Behavior in Disc-Shaped Traps -- The Charged Bose Gas, the One- and Two-Component Cases -- Bose-Einstein Quantum Phase Transition in an Optical Lattice Model En línea: http://dx.doi.org/10.1007/b137508 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35328 Ejemplares
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Título : Vortices in Bose—Einstein Condensates Tipo de documento: documento electrónico Autores: Amandine Aftalion ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Colección: Progress in Nonlinear Differential Equations and Their Applications num. 67 Número de páginas: XII, 203 p. 18 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4492-5 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Applied mathematics Engineering Physics Continuum physics Condensed matter Superconductivity Superconductors Differential Equations Strongly Correlated Systems, Mathematical Methods in Matter Classical Applications of Clasificación: 51 Matemáticas Resumen: Since the first experimental achievement of Bose–Einstein condensates (BEC) in 1995 and the award of the Nobel Prize for Physics in 2001, the properties of these gaseous quantum fluids have been the focus of international interest in physics. This monograph is dedicated to the mathematical modelling of some specific experiments which display vortices and to a rigorous analysis of features emerging experimentally. In contrast to a classical fluid, a quantum fluid such as a Bose–Einstein condensate can rotate only through the nucleation of quantized vortices beyond some critical velocity. There are two interesting regimes: one close to the critical velocity, where there is only one vortex that has a very special shape; and another one at high rotation values, for which a dense lattice is observed. One of the key features related to superfluidity is the existence of these vortices. We address this issue mathematically and derive information on their shape, number, and location. In the dilute limit of these experiments, the condensate is well described by a mean field theory and a macroscopic wave function solving the so-called Gross–Pitaevskii equation. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. We prove existence of solutions that have properties consistent with the experimental observations. Open problems related to recent experiments are presented. The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum fluids, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments Nota de contenido: The Physical Experiment and Their Mathematical Modeling -- The Mathematical Setting: A Survey of the Main Theorems -- Two-Dimensional Model for otating Condensate -- Other Trapping Potentials -- High-Velocity and Quantam Hall Regime -- Three-Dimensional Rotating Condensate -- Superfluid Flow Around an Obstacle -- Further Open Problems En línea: http://dx.doi.org/10.1007/0-8176-4492-X Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34873 Vortices in Bose—Einstein Condensates [documento electrónico] / Amandine Aftalion ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2006 . - XII, 203 p. 18 illus : online resource. - (Progress in Nonlinear Differential Equations and Their Applications; 67) .
ISBN : 978-0-8176-4492-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Applied mathematics Engineering Physics Continuum physics Condensed matter Superconductivity Superconductors Differential Equations Strongly Correlated Systems, Mathematical Methods in Matter Classical Applications of Clasificación: 51 Matemáticas Resumen: Since the first experimental achievement of Bose–Einstein condensates (BEC) in 1995 and the award of the Nobel Prize for Physics in 2001, the properties of these gaseous quantum fluids have been the focus of international interest in physics. This monograph is dedicated to the mathematical modelling of some specific experiments which display vortices and to a rigorous analysis of features emerging experimentally. In contrast to a classical fluid, a quantum fluid such as a Bose–Einstein condensate can rotate only through the nucleation of quantized vortices beyond some critical velocity. There are two interesting regimes: one close to the critical velocity, where there is only one vortex that has a very special shape; and another one at high rotation values, for which a dense lattice is observed. One of the key features related to superfluidity is the existence of these vortices. We address this issue mathematically and derive information on their shape, number, and location. In the dilute limit of these experiments, the condensate is well described by a mean field theory and a macroscopic wave function solving the so-called Gross–Pitaevskii equation. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. We prove existence of solutions that have properties consistent with the experimental observations. Open problems related to recent experiments are presented. The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum fluids, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments Nota de contenido: The Physical Experiment and Their Mathematical Modeling -- The Mathematical Setting: A Survey of the Main Theorems -- Two-Dimensional Model for otating Condensate -- Other Trapping Potentials -- High-Velocity and Quantam Hall Regime -- Three-Dimensional Rotating Condensate -- Superfluid Flow Around an Obstacle -- Further Open Problems En línea: http://dx.doi.org/10.1007/0-8176-4492-X Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34873 Ejemplares
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