A Computational Non Commutative Geometry Program For Disordered Topological Insulators

Download A Computational Non Commutative Geometry Program For Disordered Topological Insulators full books in PDF, epub, and Kindle. Read online A Computational Non Commutative Geometry Program For Disordered Topological Insulators ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

A Computational Non-commutative Geometry Program for Disordered Topological Insulators

Author : Emil Prodan
Publisher : Springer
ISBN 13 : 3319550233
Total Pages : 123 pages
Book Rating : 4.3/5 (195 download)

DOWNLOAD NOW!

Book Synopsis A Computational Non-commutative Geometry Program for Disordered Topological Insulators by : Emil Prodan

Download or read book A Computational Non-commutative Geometry Program for Disordered Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2017-03-17 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a computational program based on the principles of non-commutative 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 non-commutative 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 finite-volume approximation of the non-commutative 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 canonical-finite 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.

Cyclic Cohomology at 40: Achievements and Future Prospects

Author : A. Connes
Publisher : American Mathematical Society
ISBN 13 : 1470469774
Total Pages : 592 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Cyclic Cohomology at 40: Achievements and Future Prospects by : A. Connes

Download or read book Cyclic Cohomology at 40: Achievements and Future Prospects written by A. Connes and published by American Mathematical Society. This book was released on 2023-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.

Geometric Methods in Physics XXXVIII

Author : Piotr Kielanowski
Publisher : Springer Nature
ISBN 13 : 3030533050
Total Pages : 373 pages
Book Rating : 4.0/5 (35 download)

DOWNLOAD NOW!

Book Synopsis Geometric Methods in Physics XXXVIII by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Springer Nature. This book was released on 2020-10-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems

Author : Hermann Schulz-Baldes
Publisher : Springer Nature
ISBN 13 : 3031122011
Total Pages : 225 pages
Book Rating : 4.0/5 (311 download)

DOWNLOAD NOW!

Book Synopsis Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems by : Hermann Schulz-Baldes

Download or read book Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems written by Hermann Schulz-Baldes and published by Springer Nature. This book was released on 2022-12-31 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.

A Response Theory of Topological Insulators

Author : Wing Fung Leung
Publisher :
ISBN 13 :
Total Pages : 117 pages
Book Rating : 4.:/5 (87 download)

DOWNLOAD NOW!

Book Synopsis A Response Theory of Topological Insulators by : Wing Fung Leung

Download or read book A Response Theory of Topological Insulators written by Wing Fung Leung and published by . This book was released on 2013 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: A time-reversal invariant topological insulator is defined by its topological magnetoelectric response that is robust against disorder. The response formula, defined on a Brillouin torus, defines a $mathbb{Z}_2$ invariant and classifies the topological phase. However, in the presence of disorder or the magnetic field, the notion of Brillouin torus is destroyed and the response formula is no longer well-defined. This has been a challenging open problem, and it is essental in defining a topological insulator. This thesis proposes a topological response theory that is free from this fundamental deficiency. We derived the magnetoelectric response formula in position space for a generic three dimensional model under disorder and finite magnetic field. For time-reversal invariant systems, we connected the result to the 2nd Chern number in Noncommutative Geometry. We developed the noncommutative theory of Chern numbers and showed that the quantization of the magnetoelectric response is robust against disorder. Numerical studies on serveral disodered topological models in 1D and 3D are presented.

Topological Insulators

Author : Shun-Qing Shen
Publisher : Springer
ISBN 13 : 9783642439513
Total Pages : 0 pages
Book Rating : 4.4/5 (395 download)

DOWNLOAD NOW!

Book Synopsis Topological Insulators by : Shun-Qing Shen

Download or read book Topological Insulators written by Shun-Qing Shen and published by Springer. This book was released on 2012-12-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.

Bulk and Boundary Invariants for Complex Topological Insulators

Author : Emil Prodan
Publisher : Springer
ISBN 13 : 3319293516
Total Pages : 217 pages
Book Rating : 4.3/5 (192 download)

DOWNLOAD NOW!

Book Synopsis Bulk and Boundary Invariants for Complex Topological Insulators by : Emil Prodan

Download or read book Bulk and Boundary Invariants for Complex Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2016-02-05 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.

The Role of Topology in Materials

Author : Sanju Gupta
Publisher :
ISBN 13 : 9783319765976
Total Pages : 297 pages
Book Rating : 4.7/5 (659 download)

DOWNLOAD NOW!

Book Synopsis The Role of Topology in Materials by : Sanju Gupta

Download or read book The Role of Topology in Materials written by Sanju Gupta and published by . This book was released on 2018 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure-property-function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

Condensed Matter Field Theory

Author : Alexander Altland
Publisher : Cambridge University Press
ISBN 13 : 0521769752
Total Pages : 785 pages
Book Rating : 4.5/5 (217 download)

DOWNLOAD NOW!

Book Synopsis Condensed Matter Field Theory by : Alexander Altland

Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Geometric Methods in Physics XXXVIII

Author : Piotr Kielanowski
Publisher : Birkhäuser
ISBN 13 : 9783030533045
Total Pages : 381 pages
Book Rating : 4.5/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Geometric Methods in Physics XXXVIII by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Birkhäuser. This book was released on 2020-10-28 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Statistical Mechanics

Author : James Sethna
Publisher : OUP Oxford
ISBN 13 : 0191566217
Total Pages : 374 pages
Book Rating : 4.1/5 (915 download)

DOWNLOAD NOW!

Book Synopsis Statistical Mechanics by : James Sethna

Download or read book Statistical Mechanics written by James Sethna and published by OUP Oxford. This book was released on 2006-04-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

K-Theory for Operator Algebras

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
ISBN 13 : 1461395720
Total Pages : 347 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!

Book Synopsis K-Theory for Operator Algebras by : Bruce Blackadar

Download or read book K-Theory for Operator Algebras written by Bruce Blackadar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

Introduction to Stochastic Analysis

Author : Vigirdas Mackevicius
Publisher : John Wiley & Sons
ISBN 13 : 1118603249
Total Pages : 220 pages
Book Rating : 4.1/5 (186 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Stochastic Analysis by : Vigirdas Mackevicius

Download or read book Introduction to Stochastic Analysis written by Vigirdas Mackevicius and published by John Wiley & Sons. This book was released on 2013-02-07 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.

Modern Condensed Matter

Author :
Publisher :
ISBN 13 : 9780957481190
Total Pages : 15 pages
Book Rating : 4.4/5 (811 download)

DOWNLOAD NOW!

Book Synopsis Modern Condensed Matter by :

Download or read book Modern Condensed Matter written by and published by . This book was released on 2020 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mathematics and Topology of Fullerenes

Author : Franco Cataldo
Publisher : Springer Science & Business Media
ISBN 13 : 9400702213
Total Pages : 294 pages
Book Rating : 4.4/5 (7 download)

DOWNLOAD NOW!

Book Synopsis The Mathematics and Topology of Fullerenes by : Franco Cataldo

Download or read book The Mathematics and Topology of Fullerenes written by Franco Cataldo and published by Springer Science & Business Media. This book was released on 2011-12-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.

Discrete and Topological Models in Molecular Biology

Author : Nataša Jonoska
Publisher : Springer Science & Business Media
ISBN 13 : 3642401937
Total Pages : 522 pages
Book Rating : 4.6/5 (424 download)

DOWNLOAD NOW!

Book Synopsis Discrete and Topological Models in Molecular Biology by : Nataša Jonoska

Download or read book Discrete and Topological Models in Molecular Biology written by Nataša Jonoska and published by Springer Science & Business Media. This book was released on 2013-12-23 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.

Classical and Quantum Physics

Author : G. Marmo
Publisher : Springer
ISBN 13 : 9783030247478
Total Pages : 0 pages
Book Rating : 4.2/5 (474 download)

DOWNLOAD NOW!

Book Synopsis Classical and Quantum Physics by : G. Marmo

Download or read book Classical and Quantum Physics written by G. Marmo and published by Springer. This book was released on 2019-10-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.