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Author  Title  Accn#  Year  Item Type  Claims 
1 
Moshayedi, Nima 
Quantum Field Theory and Functional Integrals 
I12798 
2023 
eBook 

2 
Isozaki, Hiroshi 
ManyBody Schr??dinger Equation 
I12665 
2023 
eBook 

3 
Tornetta, Gabriele Nunzio 
Mathematical Quantum Physics 
I12251 
2022 
Book 

4 
Emamirad, Hassan 
Scattering Theory for Transport Phenomena 
I11839 
2021 
eBook 

5 
Capozziello, Salvatore 
A Mathematical Journey to Quantum Mechanics 
I11789 
2021 
eBook 

6 
Hiai, Fumio 
Quantum fDivergences in von Neumann Algebras 
I11715 
2021 
eBook 

7 
Alabiso, Carlo 
A Primer on Hilbert Space Theory 
I11622 
2021 
eBook 

8 
De Nittis, Giuseppe 
Linear Response Theory 
I10402 
2017 
eBook 

9 
Prodan, Emil 
A Computational Noncommutative Geometry Program for Disordered Topological Insulators 
I10352 
2017 
eBook 

10 
Bru, J.B 
LiebRobinson Bounds for MultiCommutators and Applications to Response Theory 
I10275 
2017 
eBook 


2.


Title  ManyBody Schr??dinger Equation : Scattering Theory and Eigenfunction Expansions 
Author(s)  Isozaki, Hiroshi 
Publication  Singapore, 1. Imprint: Springer
2. Springer Nature Singapore, 2023. 
Description  XVII, 399 p. 10 illus : online resource 
Abstract Note  Spectral properties for Schr??dinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the fewparticle systems, we now have sufficient knowledge for twobody systems, although much less is known about Nbody systems. The asymptotic completeness of timedependent wave operators was proved in the 1980s and was a landmark in the study of the Nbody problem. However, many problems are left open for the stationary Nparticle equation. Due to the recent rapid development of computer power, it is now possible to compute the threebody scattering problem numerically, in which the stationary formulation of scattering is used. This means that the stationary theory for Nbody Schr??dinger operators remains an important problem of quantum mechanics. It is stressed here that for the threebody problem, we have a satisfactory stationary theory. This book is devoted to the mathematical aspects of the Nbody problem from both the timedependent and stationary viewpoints. The main themes are: (1) The Mourre theory for the resolvent of selfadjoint operators (2) Twobody Schr??dinger operators???Timedependent approach and stationary approach (3) Timedependent approach to Nbody Schr??dinger operators (4) Eigenfunction expansion theory for threebody Schr??dinger operators Compared with existing books for the manybody problem, the salient feature of this book consists in the stationary scattering theory (4). The eigenfunction expansion theorem is the physical basis of Schr??dinger operators. Recently, it proved to be the basis of inverse problems of quantum scattering. This book provides necessary background information to understand the physical and mathematical basis of Schr??dinger operators and standard knowledge for future development. 
ISBN,Price  9789819937042 
Keyword(s)  1. DIFFERENTIAL EQUATIONS
2. EBOOK  SPRINGER
3. FUNCTIONAL ANALYSIS
4. MATHEMATICAL PHYSICS
5. QUANTUM PHYSICS

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I12665 


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3.


Title  Mathematical Quantum Physics : A Foundational Introduction 
Author(s)  Tornetta, Gabriele Nunzio 
Publication  Cham, 1. Imprint: Springer
2. Springer International Publishing, 2022. 
Description  XI, 181 p. 5 illus : online resource 
Abstract Note  This book provides the rigorous mathematical foundations of Quantum Physics, from the operational meaning of the measuring process to the most recent theories for the quantum scale of spacetime geometry. Topics like relativistic invariance, quantum systems with finite and infinitely many degrees of freedom, second quantisation, scattering theory, are all presented through the formalism of Operator Algebras for a precise mathematical justification. The book is targeted to graduate students and researchers in the area of theoretical/mathematical physics who want to learn about the mathematical foundations of quantum physics, as well as the mathematics students and researchers in the area of operator algebras/functional analysis who want to dive into some of the applications of the theory to physics. 
ISBN,Price  9783031148125 
Keyword(s)  1. EBOOK
2. EBOOK  SPRINGER
3. FUNCTIONAL ANALYSIS
4. Mathematical Methods in Physics
5. MATHEMATICAL PHYSICS
6. QUANTUM PHYSICS

Item Type  Book 
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Call#  Status  Issued To  Return Due On  Physical Location 
I12251 


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4.


Title  Scattering Theory for Transport Phenomena 
Author(s)  Emamirad, Hassan 
Publication  Singapore, Springer Nature Singapore, 2021. 
Description  XXI, 179 p. 6 illus : online resource 
Abstract Note  The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*algebra, different types of semigroups, Schatten???von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland???s formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schr??dinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen 
ISBN,Price  9789811623738 
Keyword(s)  1. EBOOK
2. EBOOK  SPRINGER
3. FUNCTIONAL ANALYSIS
4. MATHEMATICAL PHYSICS
5. QUANTUM PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I11839 


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5.


Title  A Mathematical Journey to Quantum Mechanics 
Author(s)  Capozziello, Salvatore;Boskoff, WladimirGeorges 
Publication  Cham, Springer International Publishing, 2021. 
Description  XV, 289 p. 10 illus. in color : online resource 
Abstract Note  This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the doublesplit, atomic spectra, and photoelectric effect. The Schr??dinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered. The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 selfcontained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020 
ISBN,Price  9783030860981 
Keyword(s)  1. Atomic and Molecular Structure and Properties
2. Atomic structure????
3. EBOOK
4. EBOOK  SPRINGER
5. FUNCTIONAL ANALYSIS
6. MATHEMATICAL PHYSICS
7. Molecular structure??
8. QUANTUM PHYSICS
9. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I11789 


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6.


Title  Quantum fDivergences in von Neumann Algebras : Reversibility of Quantum Operations 
Author(s)  Hiai, Fumio 
Publication  Singapore, Springer Nature Singapore, 2021. 
Description  X, 194 p. 139 illus : online resource 
Abstract Note  Relative entropy has played a significant role in various fields of mathematics and physics as the quantum version of the Kullback???Leibler divergence in classical theory. Many variations of relative entropy have been introduced so far with applications to quantum information and related subjects. Typical examples are three different classes, called the standard, the maximal, and the measured fdivergences, all of which are defined in terms of (operator) convex functions f on (0,???) and have respective mathematical and information theoretical backgrounds. The ??R??nyi relative entropy and its new version called the sandwiched ??R??nyi relative entropy have also been useful in recent developments of quantum information. In the first half of this monograph, the different types of quantum fdivergences and the R??nyitype divergences mentioned above in the general von Neumann algebra setting are presented for study. While quantum information has been developing mostly in the finitedimensional setting, it is widely believed that von Neumann algebras provide the most suitable framework in studying quantum information and related subjects. Thus, the advance of quantum divergences in von Neumann algebras will be beneficial for further development of quantum information. Quantum divergences are functions of two states (or more generally, two positive linear functionals) on a quantum system and measure the difference between the two states. They are often utilized to address such problems as state discrimination, error correction, and reversibility of quantum operations. In the second half of the monograph, the reversibility/sufficiency theory for quantum operations (quantum channels) between von Neumann algebras via quantum fdivergences is explained, thus extending and strengthening Petz' previous work. For the convenience of the reader, an appendix including concise accounts of von Neumann algebras is provided 
ISBN,Price  9789813341999 
Keyword(s)  1. EBOOK
2. EBOOK  SPRINGER
3. FUNCTIONAL ANALYSIS
4. MATHEMATICAL PHYSICS
5. OPERATOR THEORY
6. Quantum computing
7. QUANTUM INFORMATION

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Call#  Status  Issued To  Return Due On  Physical Location 
I11715 


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7.


Title  A Primer on Hilbert Space Theory : Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups 
Author(s)  Alabiso, Carlo;Weiss, Ittay 
Publication  Cham, Springer International Publishing, 2021. 
Description  XXII, 328 p. 19 illus : online resource 
Abstract Note  This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for nonrelativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but readerfriendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors???s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics 
ISBN,Price  9783030674175 
Keyword(s)  1. ALGEBRAIC TOPOLOGY
2. EBOOK
3. EBOOK  SPRINGER
4. FUNCTIONAL ANALYSIS
5. Mathematical Methods in Physics
6. MATHEMATICAL PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I11622 


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8.


Title  Linear Response Theory : An AnalyticAlgebraic Approach 
Author(s)  De Nittis, Giuseppe;Lein, Max 
Publication  Cham, Springer International Publishing, 2017. 
Description  X, 138 p : online resource 
Abstract Note  This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3???5: the relevant von Neumann algebras, noncommutative $L^p$ and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and KuboStreda formulas. The book closes with a chapter about possible future developments and applications of the theory to periodic light conductors. The book addresses a wide audience of mathematical physicists, focusing on the conceptual aspects rather than technical details and making algebraic methods accessible to analysts 
ISBN,Price  9783319567327 
Keyword(s)  1. CONDENSED MATTER
2. CONDENSED MATTER PHYSICS
3. EBOOK
4. EBOOK  SPRINGER
5. FUNCTIONAL ANALYSIS
6. Mathematical Methods in Physics
7. MATHEMATICAL PHYSICS
8. PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10402 


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9.


Title  A Computational Noncommutative Geometry Program for Disordered Topological Insulators 
Author(s)  Prodan, Emil 
Publication  Cham, Springer International Publishing, 2017. 
Description  X, 118 p. 19 illus. in color : online resource 
Abstract Note  This work presents a computational program based on the principles of noncommutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons??? dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of noncommutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finitevolume approximation of the noncommutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonicalfinite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation. The book is intended for graduate students and researchers in numerical and mathematical physics 
ISBN,Price  9783319550237 
Keyword(s)  1. CONDENSED MATTER
2. CONDENSED MATTER PHYSICS
3. EBOOK
4. EBOOK  SPRINGER
5. FUNCTIONAL ANALYSIS
6. KTHEORY
7. Mathematical Methods in Physics
8. MATHEMATICAL PHYSICS
9. PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10352 


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10.
 
Title  LiebRobinson Bounds for MultiCommutators and Applications to Response Theory 
Author(s)  Bru, J.B;de Siqueira Pedra, W 
Publication  Cham, Springer International Publishing, 2017. 
Description  VII, 109 p : online resource 
Abstract Note  LiebRobinson bounds for multicommutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of nonrelativistic quantum particles with shortrange, possibly timedependent interactions. In particular, the existence of fundamental solutions is shown for those (nonautonomous) C*dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) nonautonomous evolution equations are not given. In mathematical physics, bounds on multicommutators of an order higher than two can be used to study linear and nonlinear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics of Quantum Mechanics are presented, keeping in mind its algebraic formulation. The C*algebraic setting for lattice fermions, as well as the celebrated LiebRobinson bounds for commutators, are explained in detail, for completeness 
ISBN,Price  9783319457840 
Keyword(s)  1. CONDENSED MATTER
2. CONDENSED MATTER PHYSICS
3. EBOOK
4. EBOOK  SPRINGER
5. FUNCTIONAL ANALYSIS
6. Mathematical Methods in Physics
7. MATHEMATICAL PHYSICS
8. PHYSICS
9. QUANTUM COMPUTERS
10. Quantum Information Technology, Spintronics
11. SPINTRONICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10275 


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