Abstract:
Singularities of the density of states in one-dimensional disordered systems near
the spectrum bounds have been studied. It is shown that there exist two types of the
true bounds, fluctuational and stable ones. The density of states in the neighbourhood
of a fluctuational bound is determined by probabilistic properties of the problem. Near a stable spectrum bound the density of states as a function of the energy parameter
possisses an universal square root singularity. Specific distinctions of the problem influence
only the magnitude of the coefficient of this singularity.
Citation:
S. A. Gredeskul, L. A. Pastur, “Behavior of the density of states in one-dimensional disordered systems near the edges of the spectrum”, TMF, 23:1 (1975), 132–139; Theoret. and Math. Phys., 23:1 (1975), 404–409
\Bibitem{GrePas75}
\by S.~A.~Gredeskul, L.~A.~Pastur
\paper Behavior of the density of states in one-dimensional disordered systems near the edges of the spectrum
\jour TMF
\yr 1975
\vol 23
\issue 1
\pages 132--139
\mathnet{http://mi.mathnet.ru/tmf3792}
\transl
\jour Theoret. and Math. Phys.
\yr 1975
\vol 23
\issue 1
\pages 404--409
\crossref{https://doi.org/10.1007/BF01038225}
Linking options:
https://www.mathnet.ru/eng/tmf3792
https://www.mathnet.ru/eng/tmf/v23/i1/p132
This publication is cited in the following 12 articles:
Chiara Boccato, Joachim Kerner, Maximilian Pechmann, “Interacting many-particle systems in the random Kac–Luttinger model and proof of Bose–Einstein condensation”, Journal de Mathématiques Pures et Appliquées, 2024
Zhengqi Fu, Xiong Li, “Spectral type of a class of random Jacobi operators”, Journal of Mathematical Physics, 62:11 (2021)
Joachim Kerner, Maximilian Pechmann, Wolfgang Spitzer, “On Bose–Einstein Condensation in the Luttinger–Sy Model with Finite Interaction Strength”, J Stat Phys, 174:6 (2019), 1346
Milivoje Lukic, Darren C. Ong, “Generalized Prüfer variables for perturbations of Jacobi and CMV matrices”, Journal of Mathematical Analysis and Applications, 444:2 (2016), 1490
Maxim Drabkin, Werner Kirsch, Hermann Schulz-Baldes, “Transport in the random Kronig-Penney model”, Journal of Mathematical Physics, 53:12 (2012)
Milivoje Lukic, “Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation”, Commun. Math. Phys., 306:2 (2011), 485
Taksu Cheon, Pavel Exner, Petr Šeba, “Wave function shredding by sparse quantum barriers”, Physics Letters A, 277:1 (2000), 1
Alexander Kiselev, Christian Remling, Barry Simon, “Effective Perturbation Methods for One-Dimensional Schrödinger Operators”, Journal of Differential Equations, 151:2 (1999), 290
Yoram Last, Barry Simon, “Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum”, Journal of Functional Analysis, 154:2 (1998), 513
L. A. Pastur, “Spectral theory of random self-adjoint operators”, J. Soviet Math., 46:4 (1989), 1979–2021
S. A. Gredeskul, L. A. Pastur, “Density of states near the fluctuation boundary of the spectrum of one-dimensional incommensurable structures”, Theoret. and Math. Phys., 62:2 (1985), 213–215
Citation in format AMSBIB
Contact us: