Duke Mathematical Journal

Almost periodic Schrödinger operators II. The integrated density of states

Joseph Avron and Barry Simon

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Duke Math. J. Volume 50, Number 1 (1983), 369-391.

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B25
Secondary: 35P05: General topics in linear spectral theory 81C10


Avron, Joseph; Simon, Barry. Almost periodic Schrödinger operators II. The integrated density of states. Duke Math. J. 50 (1983), no. 1, 369--391. doi:10.1215/S0012-7094-83-05016-0. http://projecteuclid.org/euclid.dmj/1077303014.

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  • [1] S. Aubry and G. Andre, Analyticity breaking and Anderson localization in incommensurate lattices, Group theoretical methods in physics (Proc. Eighth Internat. Colloq., Kiryat Anavim, 1979), Ann. Israel Phys. Soc., vol. 3, Hilger, Bristol, 1980, pp. 133–164.
  • [2] S. Aubry, The new concept of transitions by breaking of analyticity in a crystallographic model, Solitons and condensed matter physics (Proc. Sympos. Nonlinear (Soliton) Structure and Dynamics in Condensed Matter, Oxford, 1978), Springer Ser. Solid-State Sci., vol. 8, Springer, Berlin, 1978, pp. 264–277.
  • [3] J. Avron and B. Simon, Almost periodic Schrödinger operators. I. Limit periodic potentials, Comm. Math. Phys. 82 (1981/82), no. 1, 101–120.
  • [4] J. Bellissard, A. Formoso, R. Lima, and D. Testard, A quasi-periodic interaction with a metal-insulator transition, Phys. Rev. B 26 (1982), 3024.
  • [5] J. Bellissard and D. Testard, in prep.
  • [6] M. Benderskiĭ and L. Pastur, The spectrum of the one-dimensional Schrödinger equation with random potential, Mat. Sb. (N.S.) 82 (124) (1970), 273–284.
  • [7] Ya. Goldstein, S. Molchanov, and L. Pastur, A pure point spectrum of the stochastic one-dimensional Schrödinger operator, Func. Anal. Pril 11 (1977), no. 1.
  • [8] A. Ya. Gordon, On the point spectrum of the one-dimensional Schrödinger operator, Usp. Math. Nauk. 31 (1976), 257.
  • [9] R. A. Johnson, The recurrent Hill's equation, J. Differential Equations 46 (1982), no. 2, 165–193.
  • [10] R. Johnson and J. Moser, The rotation number for almost periodic potentials, Comm. Math. Phys. 84 (1982), no. 3, 403–438.
  • [11] J. Moser, An example of a Schroedinger equation with almost periodic potential and nowhere dense spectrum, Comment. Math. Helv. 56 (1981), no. 2, 198–224.
  • [12] V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210.
  • [13] L. A. Pastur, Spectral properties of disordered systems in the one-body approximation, Comm. Math. Phys. 75 (1980), no. 2, 179–196.
  • [14] D. Pearson, Singular continuous measures in scattering theory, Comm. Math. Phys. 60 (1978), no. 1, 13–36.
  • [15] M. Reed and B. Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York, 1972.
  • [16] G. Scharf, Almost periodic potentials, Helv. Phys. Acta. 38 (1965), 573–605.
  • [17] S. Schwartzman, Asymptotic cycles, Ann. of Math. (2) 66 (1957), 270–284.
  • [18] M. Shubin, Density of states for self-adjoint elliptic operators with almost periodic coefficients, Trudy Sem. Petrovskii 3 (1978), 243.
  • [19] B. Simon, Functional integration and quantum physics, Pure and Applied Mathematics, vol. 86, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1979.
  • [20] B. Simon, Almost periodic Schrödinger operators: a review, Adv. in Appl. Math. 3 (1982), no. 4, 463–490.
  • [21] B. Simon, Schrödinger semigroups, Bull. Am. Math. Soc., to appear.
  • [22] L. Thomas, Time dependent approach to scattering from impurities in a crystal, Comm. Math. Phys. 33 (1973), 335–343.
  • [23] D. Thouless, A relation between the density of states and range of localization for one-dimensional random system, J. Phys. C 5 (1972), 77–81.
  • [24] J. Béllissard and B. Simon, Cantor spectrum for the almost Mathieu equation, J. Funct. Anal. 48 (1982), no. 3, 408–419.