Topologically Protected States In One Dimensional Systems
Topologically Protected States In One Dimensional Systems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Topologically Protected States In One Dimensional Systems book. This book definitely worth reading, it is an incredibly well-written.
Topologically Protected States in One-dimensional Systems by Charles Fefferman,James P. Lee-Thorp,Michael I. Weinstein Pdf
We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. Our model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states we construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Topologically Protected States in One-Dimensional Systems by Charles Fefferman,James P. Lee-Thorp,M. I. Weinstein Pdf
The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Dynamics of Partial Differential Equations by C. Eugene Wayne,Michael I. Weinstein Pdf
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
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.
Topological States for New Modes of Information Storage and Transfer by Prabhakar Bandaru,Shreyam Natani Pdf
This book reviews evidence for the existence of information storing states present in specific materials systems called Topological Materials. It discusses how quantum computation, a possible technology for the future, demands unique paradigms where the information storing states are just not disturbed by classical forces. They are protected from environmental disturbance, suggesting that whatever information is stored in such states would could be safe forever. The authors explain how the topological aspect arises from the configuration or the shape of energy space. He further explains that the existence of related topological states has not been conclusively established in spite of significant experimental effort over the past decade. And The book as such illustrates the necessity for such investigations as well as application of the topological states for new computational technologies. The scope of coverage includes all the necessary mathematical and physics preliminaries (starting at the undergraduate level) enabling researchers to quickly understand the state of the art literature.
Property ($T$) for Groups Graded by Root Systems by Mikhail Ershov,Andrei Jaikin-Zapirain,Martin Kassabov Pdf
The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.
Topologically Ordered Zigzag Nanoribbon: E/2 Fractionally Charged Anyons And Spin-charge Separation by Eric Sung Ryul Yang Pdf
This is the first graduate level textbook of topologically ordered phases with emphasis on graphene zigzag nanoribbons. It also explains common properties of several other topologically ordered phases as well as the e/2 fractional charge quantization and spin-charge separation of an electron.
Graded Elastic Metamaterials for Energy Harvesting by Jacopo Maria De Ponti Pdf
This book presents a complete framework for energy harvesting technologies based on graded elastic metamaterials. First, it provides a comprehensive survey of state-of-the-art research on metamaterials for energy harvesting and then explores the theoretical wave mechanics framework, going from inhomogeneous media to graded elastic metamaterials. The framework can be used to thoroughly analyse wave propagation phenomena in beams, plates, and half-spaces and to investigate the effect of local resonance on creating bandgaps or wave mode conversions. All these concepts converge together with piezoelectric materials in the study and design of piezo-augmented arrays of resonators. The energy harvesting performances of the graded metamaterials are then compared to conventional solutions, in order to quantify their advantages for applications.
Author : Naiara V. de Paulo,Pedro A. S. Salomão Publisher : American Mathematical Soc. Page : 105 pages File Size : 42,6 Mb Release : 2018-03-19 Category : Hamiltonian systems ISBN : 9781470428013
Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R by Naiara V. de Paulo,Pedro A. S. Salomão Pdf
In this article the authors study Hamiltonian flows associated to smooth functions R R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point in the zero energy level . The Hamiltonian function near is assumed to satisfy Moser's normal form and is assumed to lie in a strictly convex singular subset of . Then for all small, the energy level contains a subset near , diffeomorphic to the closed -ball, which admits a system of transversal sections , called a foliation. is a singular foliation of and contains two periodic orbits and as binding orbits. is the Lyapunoff orbit lying in the center manifold of , has Conley-Zehnder index and spans two rigid planes in . has Conley-Zehnder index and spans a one parameter family of planes in . A rigid cylinder connecting to completes . All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to in follows from this foliation.
The primary advanced textbook for the teaching of science and engineering of nanoscale devices as used in the semiconductor, electronics, magnetics, optics and electromechanics industry.
Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.
Nonsmooth Differential Geometry–An Approach Tailored for Spaces with Ricci Curvature Bounded from Below by Nicola Gigli Pdf
The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Introduction to Topological Quantum Matter & Quantum Computation by Tudor D. Stanescu Pdf
What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid-state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture and emphasizing two major new paradigms in condensed matter physics – quantum topology and quantum information – this book is ideal for graduate students and researchers entering this field, as it allows for the fruitful transfer of ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and unveils the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the toric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Topological quantum computation is also presented using a broad perspective, which includes elements of classical and quantum information theory, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and key ideas underlying quantum computation with anyons. This new edition has been updated throughout, with exciting new discussions on crystalline topological phases, including higher-order topological insulators; gapless topological phases, including Weyl semimetals; periodically-driven topological insulators; and a discussion of axion electrodynamics in topological materials. Key Features: · Provides an accessible introduction to this exciting, cross-disciplinary area of research. · Fully updated throughout with new content on the latest result from the field. · Authored by an authority on the subject. Tudor Stanescu is a professor of Condensed Matter Theory at West Virginia University, USA. He received a B.S. in Physics from the University of Bucharest, Romania, in 1994 and a Ph.D. in Theoretical Physics from the University of Illinois at Urbana Champaign in 2002. He was a Postdoctoral Fellow at Rutgers University and at the University of Maryland from 2003 to 2009. He joined the Department of Physics and Astronomy at West Virginia University in Fall 2009. Prof. Stanescu’s research interests encompass a variety of topics in theoretical condensed matter physics including topological insulators and superconductors, topological quantum computation, ultra-cold atom systems in optical lattices, and strongly correlated materials, such as, for example, cuprate high-temperature superconductors. His research uses a combination of analytical and numerical tools and focuses on understanding the emergence of exotic states of matter in solid state and cold atom structures, for example, topological superconducting phases that host Majorana zero modes, and on investigating the possibilities of exploiting these states as physical platforms for quantum computation.
Studies on Time-reversal Invariant Topological Insulators by Joseph Maciejko Pdf
This dissertation brings together a number of topics in the theory of time-reversal invariant topological insulators. The first four chapters are devoted to the transport properties of the two-dimensional (2D) quantum spin Hall state. We explain nonlocal transport measurements in mercury telluride (HgTe) quantum wells in terms of a Landauer-Büttiker theory of helical edge transport and confirm the discovery of the quantum spin Hall state in this material. We find that decoherence can lead to backscattering without breaking microscopic time-reversal symmetry. As an example of incoherent scattering, we study a Kondo impurity in an interacting helical edge liquid. A renormalization group analysis shows the existence of an impurity quantum phase transition governed by the Luttinger parameter of the edge liquid between a local helical Fermi liquid with T^6 scaling of the low-temperature conductance, and an insulating strongly correlated phase with fractionally charged emergent excitations. In the presence of a time-reversal symmetry breaking magnetic field, it is known that even coherent scattering can lead to backscattering. Through exact numerical diagonalization we find that nonmagnetic quenched disorder has a strong localizing effect on the edge transport if the disorder strength is comparable to the bulk gap. The predicted magnetoconductance agrees qualitatively with experiment. The last two chapters are devoted to 3D topological insulators. We propose a combined magnetooptical Kerr and Faraday rotation experiment as a universal measure of the Z_2 invariant. Finally, we propose a fractional generalization of 3D topological insulators in strongly correlated systems, characterized by ground state degeneracy on topologically nontrivial spatial 3-manifolds, a quantized fractional bulk magnetoelectric polarizability without time-reversal symmetry breaking, and a halved fractional quantum Hall effect on the surface.
Fundamentals and Applications of Nonlinear Nanophotonics by Nicolae C. Panoiu Pdf
Fundamentals and Applications of Nonlinear Nanophotonics includes key concepts of nonlinear nanophotonics, computational and modeling techniques to design these materials, and the latest advances. This book addresses the scientific literature on nanophotonics while most existing books focus almost exclusively on the linear aspects of light-matter interaction at the nanoscale. Sections cover nonlinear optics of sub-wavelength photonic nanostructured materials, review nonlinear optics of bound-states in the continuum, nonlinear optics of chiral plasmonic metasurfaces, nonlinear hyperbolic nanomaterials, nonlinear topological photonics, plasmonic lattice solitons, and more. This book is suitable for academics and industry professionals working in the discipline of materials science, engineering and nanotechnology. Discusses advances in nonlinear optics research such as plasmonics, topological photonics and emerging materials Reviews the latest computational methods to model and design nonlinear photonic materials Introduces key principles of advanced concepts in nonlinear optics of bound-states in a continuum and symmetries in nonlinear nano-optics
