Abstract:
For a one-dimensional diagonally disordered chain, we study the statistics of the edge Green's function (EGF) constructed using the random matrix of the Hamiltonian of this system. We assume that the disorder is either binary or uniform. We show that the EGF distribution function is not analytic in the case of binary disorder and propose a simple algorithm for constructing this function. We calculate the EGF distribution function exactly on some interval in the case of uniform disorder and propose a simple, effective method for determining this function completely and for calculating the mean EGF. We verify all the obtained results using direct computer diagonalization and observe a good agreement.
Keywords:
disordered system, random matrix, Green's function, density of states.
Citation:
G. G. Kozlov, “Statistics of the Edge Green's Function for a One-Dimensional Disordered System with Binary or Uniform Diagonal Disorder”, TMF, 140:2 (2004), 337–352; Theoret. and Math. Phys., 140:2 (2004), 1175–1181
\Bibitem{Koz04}
\by G.~G.~Kozlov
\paper Statistics of the Edge Green's Function for a~One-Dimensional Disordered System with Binary or Uniform Diagonal Disorder
\jour TMF
\yr 2004
\vol 140
\issue 2
\pages 337--352
\mathnet{http://mi.mathnet.ru/tmf90}
\crossref{https://doi.org/10.4213/tmf90}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2046751}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...140.1182K}
\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 140
\issue 2
\pages 1175--1181
\crossref{https://doi.org/10.1023/B:TAMP.0000036547.76911.b1}
Linking options:
https://www.mathnet.ru/eng/tmf90
https://doi.org/10.4213/tmf90
https://www.mathnet.ru/eng/tmf/v140/i2/p337
This publication is cited in the following 3 articles:
Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova, “On H-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree”, Reports on Mathematical Physics, 95:1 (2025), 93
G. G. Kozlov, “Calculation of spectral dependence of Anderson criterion for 1D system with correlated diagonal disorder”, Theoret. and Math. Phys., 179:1 (2014), 500–508
Helge Glöckner, “Invariant manifolds for analytic dynamical systems over ultrametric fields”, Expositiones Mathematicae, 31:2 (2013), 116