Spectral properties of disordered systems in the one-body approximation

作者: L. A. Pastur

DOI: 10.1007/BF01222516

关键词:

摘要: The paper considers the Schrodinger equation for a single particle and its discrete analogues. Assuming that coefficients of these equations are homogeneous ergodic random fields, it is proved spectra corresponding operators their point dense with probability 1 in one-dimensional case they have no absolutely continuous component. Rather wide sufficient conditions exponential growth Cauchy solutions considered found.

参考文章(16)
Barry Simon, Michael Reed, Methods of Modern Mathematical Physics ,(1972)
Radu Balescu, Introduction to non-equilibrium statistical mechanics Lectures in Statistical Physics. ,vol. 7, pp. 149- 181 ,(1971) , 10.1007/3-540-05418-9_5
Lynn H. Loomis, The converse of the Fatou theorem for positive harmonic functions Transactions of the American Mathematical Society. ,vol. 53, pp. 239- 250 ,(1943) , 10.1090/S0002-9947-1943-0007832-1
A. Casher, J. L. Lebowitz, Heat Flow in Regular and Disordered Harmonic Chains Journal of Mathematical Physics. ,vol. 12, pp. 1701- 1711 ,(1971) , 10.1063/1.1665794
I. Ya. Gol'dshtein, S. A. Molchanov, L. A. Pastur, A pure point spectrum of the stochastic one-dimensional schrödinger operator Functional Analysis and Its Applications. ,vol. 11, pp. 1- 8 ,(1977) , 10.1007/BF01135526
E. D. Belokolos, Quantum particle in a one-dimensional deformed lattice. Estimates of the gaps in the spectrum Theoretical and Mathematical Physics. ,vol. 25, pp. 1176- 1184 ,(1975) , 10.1007/BF01040126
Hirotsugu Matsuda, Kazushige Ishii, Localization of Normal Modes and Energy Transport in the Disordered Harmonic Chain Progress of Theoretical Physics Supplement. ,vol. 45, pp. 56- 86 ,(1970) , 10.1143/PTPS.45.56