David Damanik
Fairchild Senior Research Fellow
(Note: David has moved to Rice University; click
here for his new homepage.)
Dipl.Math., Johann Wolfgang GoetheUniversität, Frankfurt, Germany, 1995
Dipl.Inform., Johann Wolfgang GoetheUniversität, Frankfurt, Germany, 1996
Dr. phil. nat., Johann Wolfgang GoetheUniversität, Frankfurt, Germany, 1998
Research Interests
Schrödinger operators, selfsimilar tilings, quasicrystal models, consequences of
complexity and disorder in spectral theory
Publications (Click here for a list of
coauthors)
 alphacontinuity properties of onedimensional quasicrystals, Commun. Math. Phys.
192 (1998), 169182
 Singular continuous spectrum for the period doubling Hamiltonian on a set of full
measure, Commun. Math. Phys. 196 (1998), 477483
 Singular continuous spectrum for a class of substitution Hamiltonians, Lett. Math.
Phys. 46 (1998), 303311
 Uniform spectral properties of onedimensional quasicrystals, I. Absence of eigenvalues
(with Daniel Lenz), Commun. Math. Phys. 207 (1999), 687696
 Uniform spectral properties of onedimensional quasicrystals, II. The Lyapunov exponent
(with Daniel Lenz), Lett. Math. Phys. 50 (1999), 245257
 Uniform spectral properties of onedimensional quasicrystals, III. alphacontinuity
(with Rowan Killip and Daniel Lenz), Commun. Math. Phys. 212 (2000), 191204
 Local symmetries in the period doubling sequence, Discrete Appl. Math. 100
(2000), 115121
 A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger
operators (with Günter Stolz), Electron. J. Diff. Eqns. 2000 (2000), No.
55, pp. 18
 Palindrome complexity bounds for primitive substitution sequences (with Douglas Zare), Discrete
Math. 222 (2000), 259267
 Substitution Hamiltonians with bounded trace map orbits, J. Math. Anal. Appl. 249
(2000), 393411
 Gordontype arguments in the spectral theory of onedimensional quasicrystals, in Directions
in Mathematical Quasicrystals, M. Baake, R. V. Moody, eds., CRM Monograph Series 13,
AMS, Providence, RI (2000), pp. 277304
 Reflection symmetries of almost periodic functions (with Rowan Killip), J. Funct.
Anal. 178 (2000), 251257
 Singular continuous spectrum for a class of substitution Hamiltonians II., Lett.
Math. Phys. 54 (2000), 2531
 Multiscale analysis implies strong dynamical localization (with Peter Stollmann), Geom.
Funct. Anal. 11 (2001), 1129
 Uniform singular continuous spectrum for the period doubling Hamiltonian, Ann. Henri
Poincare 2 (2001), 101108
 Spectral theory of Schrödinger operators with lowcomplexity potentials, Ferroelectrics
250 (2001), 143149
 Linear repetitivity, I. Uniform subadditive ergodic theorems and
applications (with Daniel Lenz), Discrete Comput. Geom. 26 (2001),
411428
 A palindromic halfline criterion for absence of eigenvalues and applications to
substitution Hamiltonians (with JeanMichel Ghez and Laurent Raymond), Ann. Henri
Poincare 2 (2001), 927939
 The index of Sturmian sequences (with Daniel Lenz), European J. Combin. 23 (2002), 2329
 Some highcomplexity Hamiltonians with purely singular continuous spectrum (with Boris
Solomyak), Ann. Henri Poincare 3 (2002), 99105
 Lyapunov exponents in continuum BernoulliAnderson models (with Robert
Sims and Günter Stolz), Operator Theory: Advances and Applications 132,
Birkhäuser, Basel (2002), pp. 121130
 Localization for onedimensional, continuum, BernoulliAnderson models (with Robert Sims
and Günter Stolz), Duke Math. J. 114 (2002),
59100
 Absence of eigenvalues for a class of Schrödinger operators on the
strip, Forum Math. 14 (2002), 797806.
 Linearly recurrent circle map subshifts and an application to
Schrödinger operators (with Boris Adamczewski), Ann. Henri Poincare 3
(2002), 10191047
 Palindrome complexity (with JeanPaul Allouche, Michael Baake and Julien Cassaigne), Theoret. Comput. Sci.
292 (2003), 931
 Powers in Sturmian sequences (with Daniel Lenz), European
J. Combin. 24 (2003), 377390
 Logdimensional spectral properties of onedimensional quasicrystals (with Michael
Landrigan), Proc. Amer. Math. Soc.
131 (2003), 22092216
 Powerlaw bounds on transfer matrices and quantum dynamics in one
dimension (with Serguei Tcheremchantsev), Commun.
Math. Phys. 236 (2003), 513534
 Variational estimates for discrete Schrödinger operators with potentials of indefinite
sign (with Dirk Hundertmark, Rowan Killip, and Barry Simon), Commun. Math. Phys.
238 (2003), 545562
 Uniform spectral properties of onedimensional quasicrystals, IV. QuasiSturmian
potentials (with Daniel Lenz), J. d'Analyse Math.
90 (2003), 115139
 Quantum dynamical bounds for onedimensional quasicrystals,
Contemp. Math. 327 (2003), 8797
 Combinatorial properties of ArnouxRauzy subshifts
and applications to Schrödinger operators (with
Luca Q. Zamboni), Rev. Math. Phys. 15 (2003), 745763
 Bound states and the Szegö condition for Jacobi matrices and
Schrödinger operators (with Dirk Hundertmark and Barry Simon), J. Funct. Anal.
205 (2003), 357379
 A version of Gordon's theorem for multidimensional Schrödinger operators, Trans. Amer. Math. Soc.
356 (2004), 495507
 Halfline eigenfunction estimates and singular continuous spectrum of zero Lebesgue
measure (with Daniel Lenz), Forum Math. 16 (2004), 109128
 Reflection symmetries and absence of eigenvalues for onedimensional
Schrödinger operators (with Dirk Hundertmark), Proc. Amer. Math. Soc. 132 (2004), 19571962
 Localization for discrete onedimensional random word models (with Robert
Sims and Günter Stolz), J. Funct. Anal. 208 (2004), 423445
 Necessary and sufficient conditions in the spectral theory of Jacobi
matrices and Schrödinger operators (with Rowan Killip and Barry Simon), Int. Math. Res. Not. (2004),
no. 22, 10871097
 Powerlaw bounds on transfer matrices and quantum dynamics in one
dimension, II (with András Sütö and Serguei Tcheremchantsev), J. Funct. Anal.
216 (2004), 362387
 Halfline Schrödinger operators with no bound states (with Rowan Killip),
Acta Math. 193 (2004), 3172
 Dynamical upper bounds for onedimensional quasicrystals,
J. Math. Anal. Appl. 303 (2005), 327341
 Ergodic potentials with a discontinuous sampling function are
nondeterministic (with Rowan Killip), Math. Res. Lett. 12
(2005), 187192
 Almost everywhere positivity of the Lyapunov exponent for the doubling
map (with Rowan Killip), Commun. Math. Phys. 257
(2005), 287290
 Schrödinger operators with few bound states (with Rowan Killip and Barry
Simon), Commun. Math. Phys. 258 (2005), 741750
 Scaling estimates for solutions and dynamical lower bounds on wavepacket
spreading (with Serguei Tcheremchantsev), J. d'Analyse Math. 97
(2005), 103131
 Generic singular spectrum for ergodic Schrödinger operators (with Artur
Avila), Duke Math. J. 130 (2005), 393400
 A criterion of Boshernitzan and uniform convergence in the
multiplicative ergodic theorem (with Daniel Lenz), Duke
Math. J. 133 (2006), 95123
 Jost functions and Jost solutions for Jacobi matrices, II. Decay and
analyticity (with Barry Simon), Int. Math. Res. Not. (2006), Article
ID 19396, 132
 Zeromeasure Cantor spectrum for Schrödinger operators with
lowcomplexity potentials (with Daniel Lenz), J. Math. Pures
Appl. 85 (2006), 671686
 Verblunsky coefficients with Coulombtype decay, J.
Approx. Theory, 139 (2006), 257268
Preprints
 Substitution dynamical systems: characterization of linear
repetitivity and applications (with Daniel Lenz), to appear in J.
Math. Anal. Appl.
psfile
pdffile
 Jost functions and Jost solutions for Jacobi matrices, I. A necessary
and sufficient condition for Szegö asymptotics (with Barry Simon) , to
appear in Invent. Math. psfile pdffile
 Strictly ergodic subshifts and associated operators, to appear in Barry
Simon Festschrift psfile pdffile
 Lower transport bounds for onedimensional continuum Schrödinger
operators (with Daniel Lenz and Günter Stolz), to appear in Math.
Ann. psfile pdffile
 Schrödinger operators with many bound states (with Christian Remling),
to appear in Duke Math. J. psfile pdffile
 Dynamical upper bounds for the Fibonacci Hamiltonian (with Serguei
Tcheremchantsev) psfile pdffile
 Upper bounds in quantum dynamics (with Serguei Tcheremchantsev) psfile pdffile

Lyapunov exponents of continuous Schrödinger cocycles over irrational
rotations (with Kristian Bjerklöv and Russell Johnson), to appear in
Ann. Mat. Pura Appl. psfile pdffile

Bound states of discrete Schrödinger operators with supercritical inverse
square
potentials (with Gerald Teschl) psfile pdffile

Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A
survey of Kotani theory and its applications, to appear in Barry Simon
Festschrift psfile
pdffile
Courses Taught
Contact Information
Email: damanik@its.caltech.edu
Phone: (626) 3954345
Fax: (626) 5851728
Mailing address: Mathematics 25337, Caltech, Pasadena, CA 91125
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