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Exactly Solvable Models in Many-body Theory

Author: Norman H. March

Publisher: World Scientific Publishing Company

Published: 2016

Total Pages: 330

ISBN-13: 9789813140141

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Low order density matrices -- Solvable models for small clusters of fermions -- Small clusters of bosons -- Anyon statistics with models -- Superconductivity and superfluidity -- Exact results for an isolated impurity in a solid -- Pair potential and many-body force models for liquids -- Anderson localization in disordered systems -- Statistical field theory: especially models of critical exponents -- Relativistic fields -- Towards quantum gravity

Book Synopsis Exactly Solvable Models in Many-body Theory by : Norman H. March

Download or read book Exactly Solvable Models in Many-body Theory written by Norman H. March and published by World Scientific Publishing Company. This book was released on 2016 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low order density matrices -- Solvable models for small clusters of fermions -- Small clusters of bosons -- Anyon statistics with models -- Superconductivity and superfluidity -- Exact results for an isolated impurity in a solid -- Pair potential and many-body force models for liquids -- Anderson localization in disordered systems -- Statistical field theory: especially models of critical exponents -- Relativistic fields -- Towards quantum gravity

Exactly Solvable Models In Many-body Theory

Author: Norman H March

Publisher: World Scientific

Published: 2016-05-27

Total Pages: 347

ISBN-13: 981314016X

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The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Book Synopsis Exactly Solvable Models In Many-body Theory by : Norman H March

Download or read book Exactly Solvable Models In Many-body Theory written by Norman H March and published by World Scientific. This book was released on 2016-05-27 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Condensed Matter Physics and Exactly Soluble Models

Author: Elliott H. Lieb

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 645

ISBN-13: 3662063905

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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.

Book Synopsis Condensed Matter Physics and Exactly Soluble Models by : Elliott H. Lieb

Download or read book Condensed Matter Physics and Exactly Soluble Models written by Elliott H. Lieb and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Condensed Matter Field Theory

Author: Alexander Altland

Publisher: Cambridge University Press

Published: 2010-03-11

Total Pages: 785

ISBN-13: 0521769752

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This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Book Synopsis Condensed Matter Field Theory by : Alexander Altland

Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Many-Body Theory of Condensed Matter Systems

Author: Michael G. Cottam

Publisher: Cambridge University Press

Published: 2020-07-30

Total Pages: 289

ISBN-13: 1108488242

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For non-specialist students and researchers, this is a broad and concise introduction to the many-body theory of condensed-matter systems.

Book Synopsis Many-Body Theory of Condensed Matter Systems by : Michael G. Cottam

Download or read book Many-Body Theory of Condensed Matter Systems written by Michael G. Cottam and published by Cambridge University Press. This book was released on 2020-07-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: For non-specialist students and researchers, this is a broad and concise introduction to the many-body theory of condensed-matter systems.

Condensed Matter Theories

Author: Feodor V. Kusmartsev

Publisher: World Scientific

Published: 2010

Total Pages: 645

ISBN-13: 9814289159

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Pt. A. Statistical mechanics, magnetism, quantum and nonlinear dynamics. The groundstates and phases of the two-dimensional fully frustrated XY model / P. Minnhagen, S. Bernhardsson and B.J. Kim. 2D Ising model with competing interactions and its application to clusters and arrays of [symbol]-rings, graphene and adiabatic quantum computing / A. O'Hare, F.V. Kusmartsev and K.I. Kugel. Concerning the equation of state for a partially ionized system / G.A. Baker Jr. Quasiclassical Fourier path integral quantum correction terms to the kinetic energy of interacting quantum many-body systems / K.A. Gernoth. Ergodicity and chaos in a system of harmonic oscillators / M.H. Lee. Chaotic modes in scale free opinion networks / F.V. Kusmartsev and K.E. Kürten. Astroid curves for a synthetic antiferromagnetic stack in an applied magnetic field / D.M. Forrester [und weitere]. Entanglement properties of quantum many-body wave functions / J.W. Clark [und weitere] -- pt. B. Fermi and Bose fluids. Topological phase transitions in strongly correlated Fermi systems / J.W. Clark, V.A. Khodel and M.V. Zverev. Deconfinement and quantum liquid crystalline states of dipolar fermions in optical lattices / S.T. Carr, J. Quintanilla and J.J. Betouras. On the "generalized Slater" approximation / J. Messud [und weitere]. Fluid helium-4 in thermal equilibrium / K.A. Gernoth and M.L. Ristig. Microscopic approach in the description of slowing of electromagnetic pulses in BEC of alkalis / Y. Slyusarenko and A. Sotnikov. Anomalous behavior of ideal Fermi gas below 2D : The "ideal quantum dot" and the Paul exclusion principle / M. Grether, M. de Llano and M.H. Lee -- pt. C. Transport theory. On the quantum Hall effect in graphene / S. Fujita [und weitere]. Modelling charge transport in DNA using transfer matrices with diagonal terms / S.A. Wells, C.-T. Shih and R.A. Römer. Similarities between embolic stroke and percolation problems / J.P. Hague. Extraordinary magnetoresistance in hybrid semiconductor-metal systems / T.H. Hewett and F.V. Kusmartsev. Topological aspects of the specific heat / C.M. Sarris and A.N. Proto. Effects of electron-electron interactions in two dimensions / S.V. Kravchenko

Book Synopsis Condensed Matter Theories by : Feodor V. Kusmartsev

Download or read book Condensed Matter Theories written by Feodor V. Kusmartsev and published by World Scientific. This book was released on 2010 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pt. A. Statistical mechanics, magnetism, quantum and nonlinear dynamics. The groundstates and phases of the two-dimensional fully frustrated XY model / P. Minnhagen, S. Bernhardsson and B.J. Kim. 2D Ising model with competing interactions and its application to clusters and arrays of [symbol]-rings, graphene and adiabatic quantum computing / A. O'Hare, F.V. Kusmartsev and K.I. Kugel. Concerning the equation of state for a partially ionized system / G.A. Baker Jr. Quasiclassical Fourier path integral quantum correction terms to the kinetic energy of interacting quantum many-body systems / K.A. Gernoth. Ergodicity and chaos in a system of harmonic oscillators / M.H. Lee. Chaotic modes in scale free opinion networks / F.V. Kusmartsev and K.E. Kürten. Astroid curves for a synthetic antiferromagnetic stack in an applied magnetic field / D.M. Forrester [und weitere]. Entanglement properties of quantum many-body wave functions / J.W. Clark [und weitere] -- pt. B. Fermi and Bose fluids. Topological phase transitions in strongly correlated Fermi systems / J.W. Clark, V.A. Khodel and M.V. Zverev. Deconfinement and quantum liquid crystalline states of dipolar fermions in optical lattices / S.T. Carr, J. Quintanilla and J.J. Betouras. On the "generalized Slater" approximation / J. Messud [und weitere]. Fluid helium-4 in thermal equilibrium / K.A. Gernoth and M.L. Ristig. Microscopic approach in the description of slowing of electromagnetic pulses in BEC of alkalis / Y. Slyusarenko and A. Sotnikov. Anomalous behavior of ideal Fermi gas below 2D : The "ideal quantum dot" and the Paul exclusion principle / M. Grether, M. de Llano and M.H. Lee -- pt. C. Transport theory. On the quantum Hall effect in graphene / S. Fujita [und weitere]. Modelling charge transport in DNA using transfer matrices with diagonal terms / S.A. Wells, C.-T. Shih and R.A. Römer. Similarities between embolic stroke and percolation problems / J.P. Hague. Extraordinary magnetoresistance in hybrid semiconductor-metal systems / T.H. Hewett and F.V. Kusmartsev. Topological aspects of the specific heat / C.M. Sarris and A.N. Proto. Effects of electron-electron interactions in two dimensions / S.V. Kravchenko

Cluster Models for Surface and Bulk Phenomena

Author: Gianfranco Pacchioni

Publisher: Springer Science & Business Media

Published: 2013-03-08

Total Pages: 683

ISBN-13: 1468460218

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It is widely recognized that an understanding of the physical and chemical properties of clusters will give a great deal of important information relevant to surface and bulk properties of condensed matter. This relevance of clusters for condensed matter is one of the major motivations for the study of atomic and molecular clusters. The changes of properties with cluster size, from small clusters containing only a few atoms to large clusters containing tens of thousands of atoms, provides a unique way to understand and to control the development of bulk properties as separated units are brought together to form an extended system. Another important use of clusters is as theoretical models of surfaces and bulk materials. The electronic wavefunctions for these cluster models have special advantages for understanding, in particular, the local properties of condensed matter. The cluster wavefunctions, obtained with molecular orbital theory, make it possible to relate chemical concepts developed to describe chemical bonds in molecules to the very closely related chemical bonding at the surface and in the bulk of condensed matter. The applications of clusters to phenomena in condensed matter is a cross-disciplinary activity which requires the interaction and collaboration of researchers in traditionally separate areas. For example, it is necessary to bring together workers whose background and expertise is molecular chemistry with those whose background is solid state physics. It is also necessary to bring together experimentalists and theoreticians.

Book Synopsis Cluster Models for Surface and Bulk Phenomena by : Gianfranco Pacchioni

Download or read book Cluster Models for Surface and Bulk Phenomena written by Gianfranco Pacchioni and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is widely recognized that an understanding of the physical and chemical properties of clusters will give a great deal of important information relevant to surface and bulk properties of condensed matter. This relevance of clusters for condensed matter is one of the major motivations for the study of atomic and molecular clusters. The changes of properties with cluster size, from small clusters containing only a few atoms to large clusters containing tens of thousands of atoms, provides a unique way to understand and to control the development of bulk properties as separated units are brought together to form an extended system. Another important use of clusters is as theoretical models of surfaces and bulk materials. The electronic wavefunctions for these cluster models have special advantages for understanding, in particular, the local properties of condensed matter. The cluster wavefunctions, obtained with molecular orbital theory, make it possible to relate chemical concepts developed to describe chemical bonds in molecules to the very closely related chemical bonding at the surface and in the bulk of condensed matter. The applications of clusters to phenomena in condensed matter is a cross-disciplinary activity which requires the interaction and collaboration of researchers in traditionally separate areas. For example, it is necessary to bring together workers whose background and expertise is molecular chemistry with those whose background is solid state physics. It is also necessary to bring together experimentalists and theoreticians.

Condensed Matter Theories

Author: Heidi Reinholz

Publisher: World Scientific

Published: 2007

Total Pages: 571

ISBN-13: 9812709584

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Annotation. This series on Condensed Matter Theories provides a forum for advanced theoretical research in quantum many-body theory. The contributions are highly interdisciplinary, emphasizing common concerns among theorists applying many-particle methods in such diverse areas as solid-state, low-temperature, statistical, nuclear, particle, and biological physics, as well as in quantum field theory, quantum information and the theory of complex systems. The book is a comprehensive collection of many significant topics in the field of condensed matter theories. Each individual contribution is preceded by an extended introduction to the topic treated. Details not normally presented in journal articles can be found in this volume.

Book Synopsis Condensed Matter Theories by : Heidi Reinholz

Condensed Matter Theories

Author: Heidi Reinholz

Publisher: World Scientific

Published: 2007

Total Pages: 571

ISBN-13: 9812709592

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This series on condensed matter theories provides a forum for advanced theoretical research in quantum many-body theory. The contributions are highly interdisciplinary, emphasizing common concerns among theorists who apply many-particle methods in such diverse areas as solid-state, low-temperature, statistical, nuclear, particle, and biological physics, as well as in quantum field theory, quantum information and the theory of complex systems. Each individual contribution is preceded by an extended introduction to the topic treated. Useful details not normally presented in journal articles can be found in this volume. Sample Chapter(s). Part A: Fermi Liquids: Pressure Comparison Between the Spherical Cellular Model and the Thomas-Fermi Model (290 KB). Contents: Condensation of Helium in Wedges (E S Hernindez et al.); Pairing in Asymmetrical Fermi Systems (K F Quader & R Liao); Quantum Boltzmann Liquids (K A Gernoth et al.); Fractionally Charged Excitations on Frustrated Lattices (E Runge et al.); On the de HaasOCoVan Alphen Oscillation in 2D (S Fujita & D L Morabito); The Concept of Correlated Density and Its Application (K Morawetz et al.); Pairing of Strongly Correlated Nucleons (W H Dickhoff); KohnOCoSham Calculations Combined with an Average Pair-Density Functional Theory (P Gori-Giorgi & A Savin); Maxent Approach to Qubits (C M Sarris et al.); Ergodic Condition and Magnetic Models (M H Lee); and other papers. Readership: Physicists, chemists and applied mathematicians interested in advanced theories of condensed matter and their applications."

Book Synopsis Condensed Matter Theories by : Heidi Reinholz

Download or read book Condensed Matter Theories written by Heidi Reinholz and published by World Scientific. This book was released on 2007 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series on condensed matter theories provides a forum for advanced theoretical research in quantum many-body theory. The contributions are highly interdisciplinary, emphasizing common concerns among theorists who apply many-particle methods in such diverse areas as solid-state, low-temperature, statistical, nuclear, particle, and biological physics, as well as in quantum field theory, quantum information and the theory of complex systems. Each individual contribution is preceded by an extended introduction to the topic treated. Useful details not normally presented in journal articles can be found in this volume. Sample Chapter(s). Part A: Fermi Liquids: Pressure Comparison Between the Spherical Cellular Model and the Thomas-Fermi Model (290 KB). Contents: Condensation of Helium in Wedges (E S Hernindez et al.); Pairing in Asymmetrical Fermi Systems (K F Quader & R Liao); Quantum Boltzmann Liquids (K A Gernoth et al.); Fractionally Charged Excitations on Frustrated Lattices (E Runge et al.); On the de HaasOCoVan Alphen Oscillation in 2D (S Fujita & D L Morabito); The Concept of Correlated Density and Its Application (K Morawetz et al.); Pairing of Strongly Correlated Nucleons (W H Dickhoff); KohnOCoSham Calculations Combined with an Average Pair-Density Functional Theory (P Gori-Giorgi & A Savin); Maxent Approach to Qubits (C M Sarris et al.); Ergodic Condition and Magnetic Models (M H Lee); and other papers. Readership: Physicists, chemists and applied mathematicians interested in advanced theories of condensed matter and their applications."

Brillouin-Wigner Methods for Many-Body Systems

Author: Stephen Wilson

Publisher: Springer Science & Business Media

Published: 2009-12-01

Total Pages: 235

ISBN-13: 9048133734

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Brillouin-Wigner Methods for Many-Body Systems gives an introduction to many-body methods in electronic structure theory for the graduate student and post-doctoral researcher. It provides researchers in many-body physics and theoretical chemistry with an account of Brillouin-Wigner methodology as it has been developed in recent years to handle the multireference correlation problem. Moreover, the frontiers of this research field are defined. This volume is of interest to atomic and molecular physicists, physical chemists and chemical physicists, quantum chemists and condensed matter theorists, computational chemists and applied mathematicians.

Book Synopsis Brillouin-Wigner Methods for Many-Body Systems by : Stephen Wilson

Download or read book Brillouin-Wigner Methods for Many-Body Systems written by Stephen Wilson and published by Springer Science & Business Media. This book was released on 2009-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brillouin-Wigner Methods for Many-Body Systems gives an introduction to many-body methods in electronic structure theory for the graduate student and post-doctoral researcher. It provides researchers in many-body physics and theoretical chemistry with an account of Brillouin-Wigner methodology as it has been developed in recent years to handle the multireference correlation problem. Moreover, the frontiers of this research field are defined. This volume is of interest to atomic and molecular physicists, physical chemists and chemical physicists, quantum chemists and condensed matter theorists, computational chemists and applied mathematicians.