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|a 1262670670
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|q (electronic bk.)
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|z 9781470423230
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|a (OCoLC)ebqac982297192
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|a (OCoLC)982297192
|z (OCoLC)1262670670
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|a ebqac4908295
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| 040 |
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|a GZM
|b eng
|e rda
|e pn
|c GZM
|d LLB
|d UIU
|d OCLCA
|d COD
|d YDX
|d EBLCP
|d COO
|d IDB
|d N$T
|d OCLCQ
|d LEAUB
|d OCLCQ
|d UKAHL
|d VT2
|d K6U
|d OCLCO
|d OCLCQ
|d OCLCO
|d OCLCL
|d OCLCQ
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| 049 |
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|a GWRE
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| 050 |
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4 |
|a QC174.17.S3
|b F44 2017
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| 100 |
1 |
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|a Fefferman, Charles,
|d 1949-
|e author.
|1 https://id.oclc.org/worldcat/entity/E39PBJth33tYPcPpC7RRCYvJXd
|
| 245 |
1 |
0 |
|a Topologically protected states in one-dimensional systems /
|c C.L. Fefferman, J.P. Lee-Thorp, M.I. Weinstein.
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| 264 |
|
1 |
|a Providence, Rhode Island :
|b American Mathematical Society,
|c 2017.
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| 264 |
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4 |
|c ©2017
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| 300 |
|
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|a 1 online resource (vii, 118 pages) :
|b illustrations
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| 336 |
|
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|a text
|b txt
|2 rdacontent
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| 337 |
|
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|a computer
|b c
|2 rdamedia
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| 338 |
|
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|a volume
|b nc
|2 rdacarrier
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| 490 |
1 |
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|a Memoirs of the American Mathematical Society,
|x 0065-9266 ;
|v volume 247, number 1173
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| 500 |
|
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|a "Volume 247, number 1173 (sixth of 7 numbers), May 2017."
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| 500 |
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|a Schrödinger equation, Dirac equation, Floquet-Bloch theory, topological protection, edge states, Hill's equation, domain wall.
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| 520 |
3 |
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|a 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.
|
| 504 |
|
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|a Includes bibliographical references (pages 117-118).
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| 505 |
0 |
0 |
|g Chapter 1.
|t Introduction and Outline
|g Chapter 2.
|t Floquet-Bloch and Fourier Analysis
|g Chapter 3.
|t Dirac Points of 1D Periodic Structures
|g Chapter 4.
|t Domain Wall Modulated Periodic Hamiltonian and Formal Derivation of Topologically Protected Bound States
|g Chapter 5.
|t Main Theorem -- Bifurcation of Topologically Protected States
|g Chapter 6.
|t Proof of the Main Theorem
|g Appendix A.
|t A Variant of Poisson Summation
|g Appendix B.
|t 1D Dirac points and Floquet-Bloch Eigenfunctions
|g Appendix C.
|t Dirac Points for Small Amplitude Potentials
|g Appendix D.
|t Genericity of Dirac Points -- 1D and 2D cases
|g Appendix E.
|t Degeneracy Lifting at Quasi-momentum Zero
|g Appendix F.
|t Gap Opening Due to Breaking of Inversion Symmetry
|g Appendix G.
|t Bounds on Leading Order Terms in Multiple Scale Expansion
|g Appendix H.
|t Derivation of Key Bounds and Limiting Relations in the Lyapunov-Schmidt Reduction.
|
| 588 |
0 |
|
|a Print version record.
|
| 650 |
|
0 |
|a Quantum theory.
|
| 650 |
|
0 |
|a Schrödinger operator.
|
| 650 |
|
0 |
|a Topology.
|
| 650 |
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0 |
|a Dirac equation.
|
| 650 |
|
7 |
|a Dirac equation
|2 fast
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| 650 |
|
7 |
|a Quantum theory
|2 fast
|
| 650 |
|
7 |
|a Schrödinger operator
|2 fast
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| 650 |
|
7 |
|a Topology
|2 fast
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| 700 |
1 |
|
|a Lee-Thorp, J. P.
|q (James P.),
|d 1987-
|e author.
|1 https://id.oclc.org/worldcat/entity/E39PCjy83Vj8f8bRByX3brJXcX
|
| 700 |
1 |
|
|a Weinstein, Michael I.,
|e author.
|
| 710 |
2 |
|
|a American Mathematical Society,
|e publisher.
|
| 758 |
|
|
|i has work:
|a Topologically protected states in one-dimensional systems (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGmJgVGRW8qKrfRGMKbG9C
|4 https://id.oclc.org/worldcat/ontology/hasWork
|
| 776 |
0 |
8 |
|i Print version:
|a Fefferman, Charles, 1949-
|t Topologically protected states in one-dimensional systems
|z 9781470423230
|w (DLC) 2017010052
|w (OCoLC)972427493
|
| 830 |
|
0 |
|a Memoirs of the American Mathematical Society ;
|v no. 1173.
|
| 856 |
4 |
0 |
|u https://ebookcentral.proquest.com/lib/ucb/detail.action?docID=4908295
|z Full Text (via ProQuest)
|
| 915 |
|
|
|a -
|
| 956 |
|
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|a Ebook Central Academic Complete
|
| 956 |
|
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|b Ebook Central Academic Complete
|
| 994 |
|
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|a 92
|b COD
|
| 998 |
|
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|b WorldCat record encoding level change
|
| 999 |
f |
f |
|i 48244b9d-d989-5b7e-8ef5-f9cb9c3034e5
|s c524747e-0c1a-5982-b6cd-8c4a02c0ae52
|
| 952 |
f |
f |
|p Can circulate
|a University of Colorado Boulder
|b Online
|c Online
|d Online
|e QC174.17.S3 F44 2017
|h Library of Congress classification
|i web
|n 1
|
