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D-Index & Metrics

Mathematics

D-Index
44
Citations
5691
World Ranking
1625
National Ranking
695

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society

Overview

David Damanik is affiliated with Rice University in the United States and has contributed extensively to the fields of Mathematics and Physics and Astronomy. Their research primarily spans mathematical physics, statistical and nonlinear physics, and computational theory and mathematics, with additional work in applied mathematics and materials chemistry.

Their research focuses on key topics including spectral theory in mathematical physics, quantum chaos and dynamical systems, numerical methods in inverse problems, advanced mathematical modeling in engineering, mathematical analysis and transform methods, advanced mathematical theories, and mathematical dynamics and fractals.

Notable recent publications include:

  • Zero Measure and Singular Continuous Spectra for Quantum Graphs, 2020, Annales Henri Poincaré
  • Spectral characteristics of Schrödinger operators generated by product systems, 2023, Journal of Spectral Theory

Other recent papers featuring collaborations with co-authors are:

  • Schrödinger operators with potentials generated by hyperbolic transformations: I-positivity of the Lyapunov exponent, 2022, Inventiones mathematicae
  • Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients, 2020, Journal of Functional Analysis
  • The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials, 2023, Geometric and Functional Analysis

Frequent co-authors include Jake Fillman, Anton Gorodetski, Artur Avila, Shuzheng Guo, and Zhenghe Zhang.

Damanik has published predominantly in venues such as arXiv (Cornell University), Journal of Spectral Theory, Journal of Functional Analysis, Communications in Mathematical Physics, and Annales Henri Poincaré.

Two editions of a book titled One-Dimensional Ergodic Schrödinger Operators were published by the American Mathematical Society, one in 2022 and another in 2025, both attributed to Damanik.

Among the recognitions received, Damanik was named a Fellow of the American Mathematical Society in 2013.

Best Publications

  • The Analytic Theory of Matrix Orthogonal Polynomials

    David Damanik;Alexander Pushnitski;Barry Simon

  • Gordon-type arguments in the spectral theory of one-dimensional quasicrystals

    D. Damanik

  • Palindrome complexity

    Jean-Paul Allouche;Michael Baake;Julien Cassaigne;David Damanik

  • Schrödinger Operators with Dynamically Defined Potentials: A Survey

    David Damanik

  • Uniform Spectral Properties of One-Dimensional Quasicrystals, III. α-Continuity

    David Damanik;Rowan Killip;Daniel Lenz

  • Perturbations of orthogonal polynomials with periodic recursion coefficients

    David Damanik;Rowan Killip;Barry Simon

  • Multi-scale analysis implies strong dynamical localization

    D. Damanik;P. Stollmann

  • Uniform spectral properties of one-dimensional quasicrystals, III. $lpha$-continuity

    David Damanik;Rowan Killip;Daniel Lenz

  • Spectral properties of Schrödinger operators arising in the study of quasicrystals

    David Damanik;Mark Embree;Anton Gorodetski

  • Schrödinger operators with dynamically defined potentials

    David Damanik

  • LOCALIZATION FOR ONE DIMENSIONAL, CONTINUUM, BERNOULLI-ANDERSON MODELS

    David Damanik;Robert Sims;Günter Stolz

  • Uniform Spectral Properties of One-Dimensional Quasicrystals, I. Absence of Eigenvalues

    David Damanik;Daniel Lenz

  • Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian

    David Damanik;Anton Gorodetski

  • The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

    David Damanik;Mark Embree;Anton Gorodetski;Serguei Tcheremchantsev

  • Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling

    Artur Avila;David Damanik

  • Singular Continuous Spectrum for a Class of Substitution Hamiltonians II

    David Damanik

  • The Fibonacci Hamiltonian

    David Damanik;Anton Gorodetski;William Yessen

  • Lyapunov Exponents and Spectral Analysis of Ergodic Schrödinger Operators: A Survey of Kotani Theory and Its Applications

    David Damanik

  • Upper bounds in quantum dynamics

    David Damanik;David Damanik;Serguei Tcheremchantsev

  • Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

    David Damanik;Serguei Tcheremchantsev

  • What is Aperiodic Order

    Michael Baake;David Damanik;Uwe Grimm

Frequent Co-Authors

Daniel Lenz
Daniel Lenz Friedrich Schiller University Jena
Barry Simon
Barry Simon California Institute of Technology
Rowan Killip
Rowan Killip University of California, Los Angeles
Artur Avila
Artur Avila University of Zurich
Michael Baake
Michael Baake Bielefeld University
Boris Solomyak
Boris Solomyak Bar-Ilan University
Yang Wang
Yang Wang Hong Kong University of Science and Technology
Wilhelm Schlag
Wilhelm Schlag Yale University
Fritz Gesztesy
Fritz Gesztesy Baylor University
Assaf Naor
Assaf Naor Princeton University

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