02611cam  22004338i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000290013305000260016208200180018810000310020624501370023726300090037426400700038330000340045333600260048733700280051333800270054149000740056850400410064250508720068350600500155553300950160553800360170058800470173665000200178365000270180365000140183065000200184470000410186470000260190577601540193185600440208585600480212919546580RPAM20170613150344.0m      b    000 0 cr/|||||||||||170613s2017    riu     ob    000 0 eng    a9781470437077 (online)  aDLCbengerdacDLCdRPAM00aQC174.17.S3bF44 201700a515/.35332231 aFefferman, Charles,d1949-10aTopologically protected states in one-dimensional systems /h[electronic resource] cC.L. Fefferman, J.P. Lee-Thorp, M.I. Weinstein.  a1705 1aProvidence, Rhode Island :bAmerican Mathematical Society,c2017.  a1 online resource (pages cm.)  atextbtxt2rdacontent  aunmediatedbn2rdamedia  avolumebnc2rdacarrier0 aMemoirs of the American Mathematical Society, x1947-6221 ; vv. 1173  aIncludes bibliographical references.00tChapter 1. Introduction and OutlinetChapter 2. Floquet-Bloch and Fourier AnalysistChapter 3. Dirac Points of 1D Periodic StructurestChapter 4. Domain Wall Modulated Periodic Hamiltonian and Formal Derivation of Topologically Protected Bound StatestChapter 5. Main Theorem -- Bifurcation of Topologically Protected StatestChapter 6. Proof of the Main TheoremtAppendix A. A Variant of Poisson SummationtAppendix B. 1D Dirac points and Floquet-Bloch EigenfunctionstAppendix C. Dirac Points for Small Amplitude PotentialstAppendix D. Genericity of Dirac Points - 1D and 2D casestAppendix E. Degeneracy Lifting at Quasi-momentum ZerotAppendix F. Gap Opening Due to Breaking of Inversion SymmetrytAppendix G. Bounds on Leading Order Terms in Multiple Scale ExpansiontAppendix H. Derivation of Key Bounds and Limiting Relations in the Lyapunov-Schmidt Reduction1 aAccess is restricted to licensed institutions  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2017  aMode of access : World Wide Web  aDescription based on print version record. 0aQuantum theory. 0aSchrčodinger operator. 0aTopology. 0aDirac equation.1 aLee-Thorp, J. P.q(James P.),d1987-1 aWeinstein, Michael I.0 iPrint version: aFefferman, Charles, 1949-tTopologically protected states in one-dimensional systems /w(DLC)   2017010052x0065-9266z97814704232304 3Contentsuhttp://www.ams.org/memo/1173/4 3Contentsuhttps://doi.org/10.1090/memo/1173