Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity

Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity

Author: Marc Henneaux

Publisher: Springer Science & Business Media

Published: 2009-04-20

Total Pages: 310

ISBN-13: 0387874992

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This article is dedicated to Claudio Bunster on the occasion of his 60th birthday. It is a great honor to take this opportunity to express my gratitude to him, who in my opinion has been the greatest national physicist ever, for his wise guidance and intrepid support through the years. As a Chilean, I can further tell that Claudio’s contributions have been well far beyond theoretical physics, helping our country to be ready to face future challenges through science. Gravity in diverse dimensions is a subject in which Claudio has done major c- tributions, encouraging in many ways the following work, that is being made along different fronts in collaboration with my colleagues Diego Correa, Gustavo Dotti, Julio Oliva and David Tempo. Thepursuitforwormholesolutions,whicharehandlesinthespacetimetopology, it is as old as General Relativity and it has appeared in theoretical physics within different subjects, ranging from the attempt of describing physics as pure geometry, as in the Einstein–Rosen bridge model of a particle [1], to the concept of “charge withoutcharge”[2],aswell asindifferentissuesconcerningthe Euclideanapproach to quantum gravity (see, e.g., [3]). More recently, the systematic study of this kind of objects was pushed forward by the works of Morris, Thorne and Yurtsever [4,5].


Many-Body Methods in Chemistry and Physics

Many-Body Methods in Chemistry and Physics

Author: Isaiah Shavitt

Publisher: Cambridge University Press

Published: 2009-08-06

Total Pages: 547

ISBN-13: 052181832X

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This book describes the mathematical and diagrammatic techniques employed in the popular many-body methods to determine molecular structure, properties and interactions.


Modern Electronic Structure Theory

Modern Electronic Structure Theory

Author: David Yarkony

Publisher: World Scientific

Published: 1995

Total Pages: 766

ISBN-13: 9812832106

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Modern Electronic Structure Theory provides a didactically oriented description of the latest computational techniques in electronic structure theory and their impact in several areas of chemistry. The book is aimed at first year graduate students or college seniors considering graduate study in computational chemistry, or researchers who wish to acquire a wider knowledge of this field.


Phase Space Methods for Degenerate Quantum Gases

Phase Space Methods for Degenerate Quantum Gases

Author: Bryan J. Dalton

Publisher: International Monographs on Ph

Published: 2015

Total Pages: 433

ISBN-13: 0199562741

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Recent experimental progress has enabled cold atomic gases to be studied at nano-kelvin temperatures, creating new states of matter where quantum degeneracy occurs - Bose-Einstein condensates and degenerate Fermi gases. Such quantum states are of macroscopic dimensions. This book presents the phase space theory approach for treating the physics of degenerate quantum gases, an approach already widely used in quantum optics. However, degenerate quantum gases involve massive bosonic and fermionic atoms, not massless photons. The book begins with a review of Fock states for systems of identical atoms, where large numbers of atoms occupy the various single particle states or modes. First, separate modes are considered, and here the quantum density operator is represented by a phase space distribution function of phase space variables which replace mode annihilation, creation operators, the dynamical equation for the density operator determines a Fokker-Planck equation for the distribution function, and measurable quantities such as quantum correlation functions are given as phase space integrals. Finally, the phase space variables are replaced by time dependent stochastic variables satisfying Langevin stochastic equations obtained from the Fokker-Planck equation, with stochastic averages giving the measurable quantities. Second, a quantum field approach is treated, the density operator being represented by a distribution functional of field functions which replace field annihilation, creation operators, the distribution functional satisfying a functional FPE, etc. A novel feature of this book is that the phase space variables for fermions are Grassmann variables, not c-numbers. However, we show that Grassmann distribution functions and functionals still provide equations for obtaining both analytic and numerical solutions. The book includes the necessary mathematics for Grassmann calculus and functional calculus, and detailed derivations of key results are provided.


Computational Intelligence Methods for Green Technology and Sustainable Development

Computational Intelligence Methods for Green Technology and Sustainable Development

Author: Yo-Ping Huang

Publisher: Springer Nature

Published: 2022-12-14

Total Pages: 685

ISBN-13: 3031196945

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This book provides readers with peer-reviewed research papers presented at the 6th International Conference on Green Technology and Sustainable Development (GTSD) held in Nha Trang City, Vietnam, from July 29 to 30, 2022. The book is original work of researchers from academia and industry focusing on the theme “Green technology and sustainable development in Industrial Revolution 4.0” not only to raise awareness of the vital importance of sustainability in education, technology, and economic development, but also to highlight the essential roles of technology innovation for the green future. The book presents a wide range of research aspects including energy engineering, electric power systems, renewable energy systems, automatic control engineering, robotics, vehicle engineering, material engineering, construction engineering, mechanical engineering, vibrations, computational analysis, numerical investigation, system failure, technological solutions in health care, and so on. Through thorough research basing on both experimental and numerical methods, the authors feature either solutions for existing problems or optimization and improvement for performance of existing methods. The collected research results could be useful alternatives and implications for industry experts, research institutions, universities, and all others who share a common interest in the future global sustainable development.


Modern Electronic Structure Theory (In 2 Parts) - Part 1

Modern Electronic Structure Theory (In 2 Parts) - Part 1

Author: David R Yarkony

Publisher: World Scientific

Published: 1995-09-28

Total Pages: 766

ISBN-13: 9814504440

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Modern Electronic Structure Theory provides a didactically oriented description of the latest computational techniques in electronic structure theory and their impact in several areas of chemistry. The book is aimed at first year graduate students or college seniors considering graduate study in computational chemistry, or researchers who wish to acquire a wider knowledge of this field.


Combinatorial properties of ladders, generalised Pont-Neuf and caterpillar diagrams in the space of coloured open Jacobi diagrams

Combinatorial properties of ladders, generalised Pont-Neuf and caterpillar diagrams in the space of coloured open Jacobi diagrams

Author: Frank Ditsche

Publisher: Lulu.com

Published: 2016

Total Pages: 256

ISBN-13: 1326809016

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This doctoral thesis is a contribution to the analysis of the combinatorics of arbitrarily coloured open Jacobi diagrams and their relationship to Vassiliev invariants. We examine J. Kneissler's five ladder relations and state them in a much more precise way. We also analyse their role in the space of colored open Jacobi diagrams. Then, we establish a sort of machinery - a language together with a toolbox of lemmata, theorems and definitions to build, manipulate and analyse coloured open Jacobi diagrams. With this, we examine the role of generalised Pont-Neuf diagrams and caterpillar diagrams. Lastly we transfer this to the uncolored case, which allows us to show that the space of open Jacobi diagrams up to first Betti number five is already contained in the module of caterpillar diagrams, considered as a module of a certain subset of Vogels' algebra. This means that Vassiliev invariants associated to these degrees do not detect knot orientation.