Localization theory in a one-dimensional disordered lattice

1975 ◽  
Vol 25 (1) ◽  
pp. 1-12 ◽  
Author(s):  
J. Chahoud ◽  
L. Ferrari ◽  
G. Russo
2014 ◽  
Vol 25 (08) ◽  
pp. 1450028 ◽  
Author(s):  
L. A. Pastur ◽  
V. V. Slavin ◽  
A. A. Krivchikov

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.


1988 ◽  
Vol 186 ◽  
pp. 521-538 ◽  
Author(s):  
Pierre Devillard ◽  
François Dunlop ◽  
Bernard Souillard

We present a theoretical study of the localization phenomenon of gravity waves by a rough bottom in a one-dimensional channel. After recalling localization theory and applying it to the shallow-water case, we give the first study of the localization problem in the framework of the full potential theory; in particular we develop a renormalized-transfer-matrix approach to this problem. Our results also yield numerical estimates of the localization length, which we compare with the viscous dissipation length. This allows the prediction of which cases localization should be observable in and in which cases it could be hidden by dissipative mechanisms.


1978 ◽  
Vol 17 (12) ◽  
pp. 4487-4494 ◽  
Author(s):  
R. C. Albers ◽  
J. E. Gubernatis

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 177-179 ◽  
Author(s):  
John A. Scales

In a series of papers Benjamin White, Ping Sheng, George Papanicolaou and others have described the application of localization theory to the study of elastic wave propagation in randomly stratified one‐dimensional (1-D) media. They describe methods for computing the localization parameters and apply the results to sonic well‐log data. In this note, I will show that, at least in the seismic band, the results of their calculations disagree with effective medium theory. This disagreement may to be due to the lack of low‐frequency information in exploration seismic data.


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