Описание: The thesis presents experimental and theoretical results about the surface dynamics and the surface Dirac fermion (DF) spectral function of the strong topological insulators Bi2Te3 and Bi2Se3.
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, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and 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 emphasizes 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 torric 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.
Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.
Автор: Bernevig B Andrei Название: Topological Insulators and Superconductors ISBN: 069115175X ISBN-13(EAN): 9780691151755 Издательство: Wiley Рейтинг: Цена: 12989.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field"--
Автор: Michieletto Название: Topological Interactions in Ring Polymers ISBN: 3319410415 ISBN-13(EAN): 9783319410418 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Ring polymers are one of the last big mysteries in polymer physics, and this thesis tackles the problem of describing their behaviour when interacting in dense solutions and with complex environments and reports key findings that help shed light on these complex issues. The systems investigated are not restricted to artificial polymer systems, but also cover biologically inspired ensembles, contributing to the broad applicability and interest of the conclusions reached. One of the most remarkable findings is the unambiguous evidence that rings inter-penetrate when in dense solutions; here this behaviour is shown to lead to the emergence of a glassy state solely driven by the topology of the constituents. This novel glassy state is unconventional in its nature and, thanks to its universal properties inherited from polymer physics, will attract the attention of a wide range of physicists in the years to come.
Описание: The thesis presents experimental and theoretical results about the surface dynamics and the surface Dirac fermion (DF) spectral function of the strong topological insulators Bi2Te3 and Bi2Se3. The experimental results reveal the presence of a strong Kohn anomaly in the measured surface phonon dispersion of a low-lying optical mode, and the absence of surface Rayleigh acoustic phonons. Fitting the experimental data to theoretical models employing phonon Matsubara functions allowed the extraction of the matrix elements of the coupling Hamiltonian and the modifications to the surface phonon propagator that are encoded in the phonon self-energy. This allowed, for the first time, calculation of phonon mode-specific DF coupling ??(q) from experimental data, with average coupling significantly higher than typical values for metals, underscoring the strong coupling between optical surface phonons and surface DFs in topological insulators. Finally, to connect to experimental results obtained from photoemission spectroscopies, an electronic (DF) Matsubara function was constructed using the determined electron-phonon matrix elements and the optical phonon dispersion. This allowed calculation of the DF spectral function and density of states, allowing for comparison with photoemission and scanning tunneling spectroscopies. The results set the necessary energy resolution and extraction methodology for calculating ? from the DF perspective.
Автор: Anne-Christine Davis; Robert Brandenberger Название: Formation and Interactions of Topological Defects ISBN: 1461357675 ISBN-13(EAN): 9781461357674 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proceedings of a NATO ASI held in Cambridge, England, August 22-September 2, 1994
Описание: Banach spaces may be finite and infinite dimensional over a field and manifolds are modelled on Banach spaces. This title reviews research in stochastic processes with values in Banach spaces, manifolds and topological groups.
Автор: Lubkin Saul Название: A Non-Hausdorff Completion ISBN: 9814667382 ISBN-13(EAN): 9789814667388 Издательство: World Scientific Publishing Рейтинг: Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M DEGREES can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.
The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces -- by replacing the cumbersome "complete tensor product" of p-adic Banach spaces, with the more sophisticated "C-complete tensor product," discussed in this book.
It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.
Название: Topological insulators ISBN: 9814613258 ISBN-13(EAN): 9789814613255 Издательство: Taylor&Francis Рейтинг: Цена: 17609.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book is the result of dynamic developments that have occurred in condensed matter physics after the recent discovery of a new class of electronic materials: topological insulators. A topological insulator is a material that behaves as a band insulator in its interior, while acting as a metallic conductor at its surface. The surface current carriers in these systems have Dirac-like nature and are protected by an intrinsic topological order, which is of great interest for both fundamental research and emerging technologies, especially in the fields of electronics, spintronics, and quantum information.
The realization of the application potential of topological insulators requires a comprehensive and deep understanding of transport processes in these novel materials. This book explores the origin of the protected Dirac-like states in topological insulators and gives an insight into some of their representative transport properties. These include the quantum spin-Hall effect, nonlocal edge transport, backscattering of helical edge and surface states, weak antilocalization, unconventional triplet p-wave superconductivity, topological bound states, and emergent Majorana fermions in Josephson junctions as well as superconducting Klein tunneling.
Автор: Adhip Agarwala Название: Excursions in Ill-Condensed Quantum Matter ISBN: 3030215105 ISBN-13(EAN): 9783030215101 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Impurities, disorder or amorphous systems – ill-condensed matter – are mostly considered inconveniences in the study of materials, which is otherwise heavily based on idealized perfect crystals. The Kondo effect and the scaling theory of localization are among the fundamental and early discoveries which revealed the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and certain discrete symmetries such as time reversal in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experimental directions. However, many of these recent developments and their implications are limited to, or by, ideas that pertain to clean systems. This thesis deals with various aspects of these new developments, but in the case of unclean systems. The author introduces new ideas such as amorphous topological insulators, fractalized metals and fractionalized spins.
The work shows the fascination of topology- and geometry-governed properties of self-rolled micro- and nanoarchitectures. The author provides an in-depth representation of the advanced theoretical and numerical models for analyzing key effects, which underlie engineering of transport, superconducting and optical properties of micro- and nanoarchitectures.
Автор: Arnold Название: Topological Methods in Hydrodynamics ISBN: 038794947X ISBN-13(EAN): 9780387949475 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications
to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups,
knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic
flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable.
Topological Methods
in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. T
e necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as
to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.
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