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Topologically Protected States in One-dimensional Systems

2017 Dirac equation
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Release : 2017
Genre : Dirac equation
Kind : eBook
Book Rating : 077/5 ( reviews)

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Book Synopsis Topologically Protected States in One-dimensional Systems by : Charles Fefferman

Download or read book Topologically Protected States in One-dimensional Systems written by Charles Fefferman. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: 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

2017-04-25 Mathematics
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Release : 2017-04-25
Genre : Mathematics
Kind : eBook
Book Rating : 235/5 ( reviews)

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Book Synopsis Topologically Protected States in One-Dimensional Systems by : Charles Fefferman

Download or read book Topologically Protected States in One-Dimensional Systems written by Charles Fefferman. This book was released on 2017-04-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nanoscale Device Physics

2017 Science
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Release : 2017
Genre : Science
Kind : eBook
Book Rating : 878/5 ( reviews)

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Book Synopsis Nanoscale Device Physics by : Sandip Tiwari

Download or read book Nanoscale Device Physics written by Sandip Tiwari. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Metamaterial Analysis and Design

2023-11-06 Mathematics
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Release : 2023-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 963/5 ( reviews)

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Book Synopsis Metamaterial Analysis and Design by : Habib Ammari

Download or read book Metamaterial Analysis and Design written by Habib Ammari. This book was released on 2023-11-06. Available in PDF, EPUB and Kindle. Book excerpt: Metamaterials are advanced composite materials which have exotic and powerful properties. Their complicated microstructures make metamaterials challenging to model, requiring the use of sophisticated mathematical techniques. This book uses a from-first-principles approach (based on boundary integral methods and asymptotic analysis) to study a class of high-contrast metamaterials. These mathematical techniques are applied to the problem of designing graded metamaterials that replicate the function of the cochlea.

Topological Aspects of Condensed Matter Physics

2017-02-16 Science
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Release : 2017-02-16
Genre : Science
Kind : eBook
Book Rating : 79X/5 ( reviews)

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Book Synopsis Topological Aspects of Condensed Matter Physics by : Claudio Chamon

Download or read book Topological Aspects of Condensed Matter Physics written by Claudio Chamon. This book was released on 2017-02-16. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.

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