scholarly journals Low eigenvalues of the entanglement Hamiltonian, localization length, and rare regions in one-dimensional disordered interacting systems

2018 ◽  
Vol 97 (11) ◽  
Author(s):  
Richard Berkovits
Keyword(s):  
Localization Length ◽  
One Dimensional ◽  
Interacting Systems ◽  
Rare Regions

scholarly journals LOCALIZED ENTANGLEMENT IN ONE-DIMENSIONAL ANDERSON MODEL

2005 ◽  
Vol 19 (11) ◽  
pp. 517-527 ◽  
Author(s):  
HAIBIN LI ◽  
XIAOGUANG WANG
Keyword(s):  
Anderson Model ◽  
Localization Length ◽  
Direct Relation ◽  
Disorder Strength ◽  
One Dimensional ◽  
Entanglement Distribution ◽  
Localization Center

The entanglement in one-dimensional Anderson model is studied. The pairwise entanglement has a direct relation to the localization length and is reduced by disorder. Entanglement distribution displays the entanglement localization. The pairwise entanglements around localization center exhibit a maximum as the disorder strength increases. The dynamics of entanglement are also investigated.

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.

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