Localization theory in a one-dimensional disordered lattice

1975 ◽  
Vol 25 (1) ◽  
pp. 1-12 ◽  
Author(s):  
J. Chahoud ◽  
L. Ferrari ◽  
G. Russo
Keyword(s):  
One Dimensional ◽  
Disordered Lattice ◽  
Localization Theory

Ground state of one-dimension repulsing particles on disordered lattice

2014 ◽  
Vol 25 (08) ◽  
pp. 1450028 ◽  
Author(s):  
L. A. Pastur ◽  
V. V. Slavin ◽  
A. A. Krivchikov
Keyword(s):  
Ground State ◽  
Domain Walls ◽  
Host Lattice ◽  
One Dimension ◽  
Weak Disorder ◽  
Interacting Particles ◽  
One Dimensional ◽  
Lattice Disorder ◽  
Disordered Lattice ◽  
The Mean

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.

Localization of gravity waves on a channel with a random bottom

1988 ◽  
Vol 186 ◽  
pp. 521-538 ◽  
Author(s):  
Pierre Devillard ◽  
François Dunlop ◽  
Bernard Souillard
Keyword(s):  
Gravity Waves ◽  
Theoretical Study ◽  
Localization Length ◽  
Full Potential ◽  
Matrix Approach ◽  
Localization Problem ◽  
One Dimensional ◽  
Localization Phenomenon ◽  
Localization Theory ◽  
Transfer Matrix Approach

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.

ac conductivity of a one-dimensional site-disordered lattice

1978 ◽  
Vol 17 (12) ◽  
pp. 4487-4494 ◽  
Author(s):  
R. C. Albers ◽  
J. E. Gubernatis
Keyword(s):  
Ac Conductivity ◽  
One Dimensional ◽  
Disordered Lattice

On the use of localization theory to characterize elastic wave propagation in randomly stratified 1-D media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 177-179 ◽  
Author(s):  
John A. Scales
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Seismic Data ◽  
Effective Medium Theory ◽  
Low Frequency ◽  
Elastic Wave Propagation ◽  
Well Log ◽  
Medium Theory ◽  
One Dimensional ◽  
Localization Theory

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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