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Author: Tobias Wirth Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN: 9783838123875 Category : Languages : en Pages : 124
Book Description
The framework of the Quantum Inverse Scattering Method is used to study the hamiltonian of the XXX and XXZ spin chain with general boundary fields. Key ingredient is the underlying algebraic structure which is a combination of the Yang-Baxter algebra and a so-called Reflection algebra including boundary fields of arbitrary direction and strength. For spin chains with diagonal boundary fields this setup has been well studied using algebraic Bethe ansatz and the inverse problem was solved by Kitanine for infinite chain lengths. These results are picked up and generalized to arbitrary lengths using non-linear integral equations. In the case of non-diagonal boundary fields the lack of a reference state or pseudo vacuum prohibits the solution by algebraic Bethe ansatz. The method of separation of variables is not constrained in that sense and is applied to the XXX chain and a spin-boson model. Finally a different approach to the case of non-diagonal boundary conditions is studied. Starting from the so-called fusion hierarchy non-linear integral equations are derived bearing the possibility to extract information about an eigenvalue of a specific state.
Author: Tobias Wirth Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN: 9783838123875 Category : Languages : en Pages : 124
Book Description
The framework of the Quantum Inverse Scattering Method is used to study the hamiltonian of the XXX and XXZ spin chain with general boundary fields. Key ingredient is the underlying algebraic structure which is a combination of the Yang-Baxter algebra and a so-called Reflection algebra including boundary fields of arbitrary direction and strength. For spin chains with diagonal boundary fields this setup has been well studied using algebraic Bethe ansatz and the inverse problem was solved by Kitanine for infinite chain lengths. These results are picked up and generalized to arbitrary lengths using non-linear integral equations. In the case of non-diagonal boundary fields the lack of a reference state or pseudo vacuum prohibits the solution by algebraic Bethe ansatz. The method of separation of variables is not constrained in that sense and is applied to the XXX chain and a spin-boson model. Finally a different approach to the case of non-diagonal boundary conditions is studied. Starting from the so-called fusion hierarchy non-linear integral equations are derived bearing the possibility to extract information about an eigenvalue of a specific state.
Author: Fabio Franchini Publisher: Springer ISBN: 3319484877 Category : Science Languages : en Pages : 186
Book Description
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Author: Yoshio Kuramoto Publisher: Cambridge University Press ISBN: 0521815983 Category : Mathematics Languages : en Pages : 487
Book Description
A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.
Author: A.N. Vasiliev Publisher: Routledge ISBN: 1351446819 Category : Science Languages : en Pages : 320
Book Description
Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quant
Author: Reinhold Blumel Publisher: Jones & Bartlett Publishers ISBN: 1449666922 Category : Science Languages : en Pages : 437
Book Description
This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.
Author: Tomislav Predavač Živković Publisher: ISBN: 9781616685973 Category : Eigenvalues Languages : en Pages : 0
Book Description
There are very few quantum systems that can be solved exactly. In most cases, one has to use some approximate method. One of the most important approximate methods is perturbation expansion. The main idea of this method is simple: if one knows the solution of some parent system, one can find the solution of the "perturbed" system. It is assumed that the system does not differ from the parent system very much, in which case "perturbation" is small. Next one expresses eigenvalues and eigenstates of the perturbed systems as a power series expansion in terms of the eigenvalues and eigenstates of the parent system. Hence in order to obtain the solution of the perturbed system, one has to know the solution of the parent system. This book offers examples and solutions to this fascinating topic.
Author: Gerald Teschl Publisher: American Mathematical Soc. ISBN: 0821846604 Category : Mathematics Languages : en Pages : 322
Book Description
Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Author: Reinhold Blumel Publisher: Jones & Bartlett Publishers ISBN: 1449655904 Category : Medical Languages : en Pages : 437
Book Description
This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.
Author: V.N. Popov Publisher: Springer Science & Business Media ISBN: 9781402003073 Category : Science Languages : en Pages : 316
Book Description
Functional integration is one of the most powerful methods of contempo rary theoretical physics, enabling us to simplify, accelerate, and make clearer the process of the theoretician's analytical work. Interest in this method and the endeavour to master it creatively grows incessantly. This book presents a study of the application of functional integration methods to a wide range of contemporary theoretical physics problems. The concept of a functional integral is introduced as a method of quantizing finite-dimensional mechanical systems, as an alternative to ordinary quantum mechanics. The problems of systems quantization with constraints and the manifolds quantization are presented here for the first time in a monograph. The application of the functional integration methods to systems with an infinite number of degrees of freedom allows one to uniquely introduce and formulate the diagram perturbation theory in quantum field theory and statistical physics. This approach is significantly simpler than the widely accepted method using an operator approach.
Author: Tobias Wirth
Author: Tobias Wirth
Author: Fabio Franchini
Author: Yoshio Kuramoto
Author: A.N. Vasiliev
Author: Reinhold Blumel
Author: Tomislav Predavač Živković
Author: Gerald Teschl
Author: Reinhold Blumel
Author: V.N. Popov
Author: Domingos Humberto Urbano Marchetti