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Mathematical Physics in One Dimension

Author : Elliott H. Lieb

Publisher : Academic Press

Page : 580 pages

File Size : 44,4 MB

Release : 2013-09-17

Category : Science

ISBN : 1483218562

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Book Description

Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.





The Interacting Boson-Fermion Model

Author : F. Iachello

Publisher : Cambridge University Press

Page : 328 pages

File Size : 39,30 MB

Release : 2005-11-03

Category : Science

ISBN : 9780521021647

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Book Description

This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. It addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed.



Structures in the Universe by Exact Methods

Author : Krzysztof Bolejko

Publisher : Cambridge University Press

Page : 257 pages

File Size : 39,54 MB

Release : 2010

Category : Science

ISBN : 0521769140

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Book Description

Reviews developments in applications of inhomogeneous models to cosmology, for graduate students and academic researchers in astrophysics.



Fueling Innovation and Discovery

Author : National Research Council

Publisher : National Academies Press

Page : 64 pages

File Size : 26,99 MB

Release : 2012-08-02

Category : Mathematics

ISBN : 0309254736

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Book Description

The mathematical sciences are part of everyday life. Modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Fueling Innovation and Discovery describes recent advances in the mathematical sciences and advances enabled by mathematical sciences research. It is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries. Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence. Prepared as part of the study on the Mathematical Sciences in 2025, a broad assessment of the current state of the mathematical sciences in the United States, Fueling Innovation and Discovery presents mathematical sciences advances in an engaging way. The report describes the contributions that mathematical sciences research has made to advance our understanding of the universe and the human genome. It also explores how the mathematical sciences are contributing to healthcare and national security, and the importance of mathematical knowledge and training to a range of industries, such as information technology and entertainment. Fueling Innovation and Discovery will be of use to policy makers, researchers, business leaders, students, and others interested in learning more about the deep connections between the mathematical sciences and every other aspect of the modern world. To function well in a technologically advanced society, every educated person should be familiar with multiple aspects of the mathematical sciences.



Topological Quantum Field Theory and Four Manifolds

Author : Jose Labastida

Publisher : Springer Science & Business Media

Page : 235 pages

File Size : 20,24 MB

Release : 2007-07-18

Category : Science

ISBN : 1402031777

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Book Description

The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.



Solvable Models in Quantum Mechanics

Author : Sergio Albeverio

Publisher : Springer Science & Business Media

Page : 458 pages

File Size : 36,14 MB

Release : 2012-12-06

Category : Science

ISBN : 3642882013

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Book Description

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.



Mathematics for Physics

Author : Michael Stone

Publisher : Cambridge University Press

Page : 821 pages

File Size : 30,48 MB

Release : 2009-07-09

Category : Science

ISBN : 1139480618

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Book Description

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.



Mathematical Physics in Theoretical Chemistry

Author : S.M. Blinder

Publisher : Elsevier

Page : 426 pages

File Size : 46,53 MB

Release : 2018-11-26

Category : Science

ISBN : 0128137010

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Book Description

Mathematical Physics in Theoretical Chemistry deals with important topics in theoretical and computational chemistry. Topics covered include density functional theory, computational methods in biological chemistry, and Hartree-Fock methods. As the second volume in the Developments in Physical & Theoretical Chemistry series, this volume further highlights the major advances and developments in research, also serving as a basis for advanced study. With a multidisciplinary and encompassing structure guided by a highly experienced editor, the series is designed to enable researchers in both academia and industry stay abreast of developments in physical and theoretical chemistry. - Brings together the most important aspects and recent advances in theoretical and computational chemistry - Covers computational methods for small molecules, density-functional methods, and computational chemistry on personal and quantum computers - Presents cutting-edge developments in theoretical and computational chemistry that are applicable to graduate students and research professionals in chemistry, physics, materials science and biochemistry



Black Holes

Author : P. D. D'Eath

Publisher :

Page : 310 pages

File Size : 46,27 MB

Release : 1996

Category : Mathematics

ISBN :

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Book Description

Black Holes are regions of space-time where the gravitational field is so strong that not even light can escape. There has been much written on black holes, however in most cases they are treated as isolated objects. The author has found a number of cases in which the interaction of a black hole with another strong-field system (such as the background universe or another black hole) could be treated analytically. This includes using the powerful method of matched asymptotic expansions. In this book the author considers these wider ranging problems and examples for the first time. This book will be widely read by all those working in gravitation, and PhD students in mathematical physics.