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Ground States of Quantum Field Models, Fumio Hiroshima


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Автор: Fumio Hiroshima
Название:  Ground States of Quantum Field Models
ISBN: 9789813293045
Издательство: Springer
Классификация:


ISBN-10: 9813293047
Обложка/Формат: Soft cover
Страницы: 136
Вес: 0.24 кг.
Дата издания: 2019
Серия: SpringerBriefs in Mathematical Physics
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 14 illustrations, black and white; xvi, 136 p. 14 illus.
Размер: 234 x 156 x 8
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: Perturbation of Embedded Eigenvalues
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:
This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli–Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. These models describe interactions between bose fields and quantum mechanical matters.
A ground state is defined as the eigenvector associated with the bottom of the spectrum of a self-adjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is non-trivial to show the existence of ground states in non-perturbative ways. We show the existence of the ground state of the Pauli–Fierz mode, the Nelson model, and the spin-boson model, and several kinds of proofs of the existence of ground states are explicitly provided. Key ingredients are compact sets and compact operators in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli–Fierz model with dipole approximation we show not only the existence of ground states but also enhanced binding. The enhanced binding means that a system for zero-coupling has no ground state but it has a ground state after turning on an interaction.
The book will be of interest to graduate students of mathematics as well as to students of the natural sciences who want to learn quantum field theory from a mathematical point of view. It begins with abstract compactness arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory: boson Fock spaces, creation operators, annihilation operators, and second quantization. This book quickly takes the reader to a level where a wider-than-usual range of quantum field theory can be appreciated, and self-contained proofs of the existence of ground states and enhanced binding are presented.

Дополнительное описание: Introduction.- Preliminaries.- The Pauli-Fierz model.- The Nelson model.- Spin-boson model.- Enhanced bindings.



Geometry of Quantum States

Автор: Bengtsson Ingemar
Название: Geometry of Quantum States
ISBN: 1107026253 ISBN-13(EAN): 9781107026254
Издательство: Cambridge Academ
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Цена: 13779.00 р.
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Описание: The second edition of a book that has become a standard reference for researchers working on geometric aspects of quantum entanglement and quantum theory of information. Its comprehensive style makes it suitable for students of physics, information science, and mathematics wishing to learn more about quantum mechanics and quantum entanglement.

Low-Dimensional Models in Statistical Physics and Quantum Field Theory

Автор: Harald Grosse; Ludwig Pittner
Название: Low-Dimensional Models in Statistical Physics and Quantum Field Theory
ISBN: 3662140683 ISBN-13(EAN): 9783662140680
Издательство: Springer
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Цена: 15672.00 р.
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Описание: The main items can be grouped into integrable (quantum) spin systems, which lead in the continuum limit to (conformal invariant) quantum field theory models and their algebraic structures, ranging from the Yang-Baxter equation and quantum groups to noncommutative geometry.

Elements of Statistical Mechanics: With an Introduction to Quantum Field Theory and Numerical Simulation

Автор: Sachs
Название: Elements of Statistical Mechanics: With an Introduction to Quantum Field Theory and Numerical Simulation
ISBN: 0521143640 ISBN-13(EAN): 9780521143646
Издательство: Cambridge Academ
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Цена: 5386.00 р.
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Описание: A concise 2006 introduction to key concepts and tools of statistical mechanics. Self-contained, it combines analytical and numerical techniques, and presents a diverse range of applications. Built on many years` teaching experience, this textbook is ideal for advanced students across the physical sciences.

Quantum Mechanical Models of Metal Surfaces and Nanoparticles

Автор: Wolfgang Gr?fe
Название: Quantum Mechanical Models of Metal Surfaces and Nanoparticles
ISBN: 3319197630 ISBN-13(EAN): 9783319197630
Издательство: Springer
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Цена: 7836.00 р.
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Описание: This book proposes two simple quantum mechanical models for the analytical description of metal surfaces and nanoparticles. It gives an ostensive picture of the forces acting in a metal surface and deduces analytical formulae for the description of their physical properties.

Formulation of Statistical Mechanics Based on Thermal Pure Quantum States

Автор: Sho Sugiura
Название: Formulation of Statistical Mechanics Based on Thermal Pure Quantum States
ISBN: 9811015058 ISBN-13(EAN): 9789811015052
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This thesis introduces the concept of "thermal pure quantum (TPQ) states", which are pure quantum states in equilibrium.

Quantum Non-linear Sigma-Models

Автор: Sergei V. Ketov
Название: Quantum Non-linear Sigma-Models
ISBN: 3642086888 ISBN-13(EAN): 9783642086885
Издательство: Springer
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Цена: 14365.00 р.
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Описание: This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.

Exotic States in Quantum Nanostructures

Автор: Sarben Sarkar
Название: Exotic States in Quantum Nanostructures
ISBN: 9048161797 ISBN-13(EAN): 9789048161799
Издательство: Springer
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Цена: 26552.00 р.
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Описание: The topics range from the newly emerging area of quantum computers and quantum information using Josephson junctions to the formal mathematical methods of conformal field theory which are applied to the understanding of Luttinger liquids.

Models of quantum matter

Автор: Eckle, Hans-peter (adjunct Professor, Adjunct Professor, Humboldt Study Centre, Ulm University, Germany)
Название: Models of quantum matter
ISBN: 0199678839 ISBN-13(EAN): 9780199678839
Издательство: Oxford Academ
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Цена: 17820.00 р.
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Описание: The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.

Quantum Physics: States, Observables and Their Time Evolution

Автор: Bohm Arno, Kielanowski Piotr, Mainland G. Bruce
Название: Quantum Physics: States, Observables and Their Time Evolution
ISBN: 9402417583 ISBN-13(EAN): 9789402417586
Издательство: Springer
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Цена: 11878.00 р.
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Описание: This is an introductory graduate course on quantum mechanics, which is presented in its general form by stressing the operator approach.

Representations of the algebra of the harmonic oscillator and of the algebra of angular momentum are determined in chapters 1 and 2 respectively. The algebra of angular momentum is enlarged by adding the position operator so that the algebra can be used to describe rigid and non-rigid rotating molecules. The combination of quantum physical systems using direct-product spaces is discussed in chapter 3. The theory is used to describe a vibrating rotator, and the theoretical predictions are then compared with data for a vibrating and rotating diatomic molecule. The formalism of first- and second-order non-degenerate perturbation theory and first-order degenerate perturbation theory are derived in chapter 4. Time development is described in chapter 5 using either the Schroedinger equation of motion or the Heisenberg’s one.
An elementary mathematical tutorial forms a useful appendix for the readers who don’t have prior knowledge of the general mathematical structure of quantum mechanics.
Strong Fermion Interactions in Fractional Quantum Hall States

Автор: Shashikant Mulay; John J. Quinn; Mark Shattuck
Название: Strong Fermion Interactions in Fractional Quantum Hall States
ISBN: 3030004937 ISBN-13(EAN): 9783030004934
Издательство: Springer
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Цена: 13974.00 р.
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Описание:

This monograph presents an intuitive theory of trial wave functions for strongly interacting fermions in fractional quantum Hall states. The correlation functions for the proposed fermion interactions follow a novel algebraic approach that harnesses the classical theory of invariants and semi-invariants of binary forms. This approach can be viewed as a fitting and far-reaching generalization of Laughlin’s approach to trial wave functions. Aesthetically viewed, it illustrates an attractive symbiosis between the theory of invariants and the theory of correlations. Early research into numerical diagonalization computations for small numbers of electrons shows strong agreement with the constructed trial wave functions.
The monograph offers researchers and students of condensed matter physics an accessible discussion of this interesting area of research.
Quantum-Like Models for Information Retrieval and Decision-Making

Автор: Diederik Aerts; Andrei Khrennikov; Massimo Melucci
Название: Quantum-Like Models for Information Retrieval and Decision-Making
ISBN: 3030259129 ISBN-13(EAN): 9783030259129
Издательство: Springer
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Цена: 13974.00 р.
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Описание:

Recent years have been characterized by tremendous advances in quantum information and communication, both theoretically and experimentally. In addition, mathematical methods of quantum information and quantum probability have begun spreading to other areas of research, beyond physics. One exciting new possibility involves applying these methods to information science and computer science (without direct relation to the problems of creation of quantum computers).
The aim of this Special Volume is to encourage scientists, especially the new generation (master and PhD students), working in computer science and related mathematical fields to explore novel possibilities based on the mathematical formalisms of quantum information and probability. The contributing authors, who hail from various countries, combine extensive quantum methods expertise with real-world experience in application of these methods to computer science. The problems considered chiefly concern quantum information-probability based modeling in the following areas: information foraging; interactive quantum information access; deep convolutional neural networks; decision making; quantum dynamics; open quantum systems; and theory of contextual probability.
The book offers young scientists (students, PhD, postdocs) an essential introduction to applying the mathematical apparatus of quantum theory to computer science, information retrieval, and information processes.
Non-equilibrium Many-body States in Carbon Nanotube Quantum Dots

Автор: Tokuro Hata
Название: Non-equilibrium Many-body States in Carbon Nanotube Quantum Dots
ISBN: 981137659X ISBN-13(EAN): 9789811376597
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This book presents the first experiment revealing several unexplored non-equilibrium properties of quantum many-body states, and addresses the interplay between the Kondo effect and superconductivity by probing shot noise. In addition, it describes in detail nano-fabrication techniques for carbon nanotube quantum dots, and a measurement protocol and principle that probes both equilibrium and non-equilibrium quantum states of electrons.The book offers various reviews of topics in mesoscopic systems: shot noise measurement, carbon nanotube quantum dots, the Kondo effect in quantum dots, and quantum dots with superconducting leads, which are relevant to probing non-equilibrium physics. These reviews offer particularly valuable resources for readers interested in non-equilibrium physics in mesoscopic systems. Further, the cutting-edge experimental results presented will allow reader to catch up on a vital new trend in the field.


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