scholarly journals Localization transition, spectrum structure, and winding numbers for one-dimensional non-Hermitian quasicrystals

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Yanxia Liu ◽  
Qi Zhou ◽  
Shu Chen
Keyword(s):  
Localization Transition ◽  
One Dimensional ◽  
Spectrum Structure

Geometric discord characterize localization transition in the one-dimensional systems

2013 ◽  
Vol 67 (6) ◽  
Author(s):  
W.W. Cheng ◽  
L.Y. Gong ◽  
C.J. Shan ◽  
Y.B. Sheng ◽  
S.M. Zhao
Keyword(s):  
Localization Transition ◽  
One Dimensional ◽  
The One

scholarly journals A new eigenvalue problem for the difference operator with nonlocal conditions

2019 ◽  
Vol 24 (3) ◽  
pp. 462-484
Author(s):  
Mifodijus Sapagovas ◽  
Regimantas Ciupaila ◽  
Kristina Jakubelienė ◽  
Stasys Rutkauskas
Keyword(s):  
Eigenvalue Problem ◽  
Difference Operator ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Theoretical Expression ◽  
Difference Problem ◽  
One Dimensional ◽  
The Difference ◽  
Degenerate Matrix ◽  
Spectrum Structure

In the paper, the spectrum structure of one-dimensional differential operator with nonlocal conditions and of the difference operator, corresponding to it, has been exhaustively investigated. It has been proved that the eigenvalue problem of difference operator is not equivalent to that of matrix eigenvalue problem Au = λu, but it is equivalent to the generalized eigenvalue problem Au = λBu with a degenerate matrix B. Also, it has been proved that there are such critical values of nonlocal condition parameters under which the spectrum of both the differential and difference operator are continuous. It has been established that the number of eigenvalues of difference problem depends on the values of these parameters. The condition has been found under which the spectrum of a difference problem is an empty set. An elementary example, illustrating theoretical expression, is presented.

Delocalization-localization transition in a one-dimensional two-band model with random clusters

1999 ◽  
Vol 11 (35) ◽  
pp. 6793-6802
Author(s):  
Xiaoshuang Chen ◽  
Shi-Jie Xiong ◽  
Wei Lu ◽  
S C Shen ◽  
Akio Sasaki
Keyword(s):  
Band Model ◽  
Localization Transition ◽  
One Dimensional ◽  
Two Band Model

scholarly journals Topological Superconductor to Anderson Localization Transition in One-Dimensional Incommensurate Lattices

2013 ◽  
Vol 110 (17) ◽  
Author(s):  
Xiaoming Cai ◽  
Li-Jun Lang ◽  
Shu Chen ◽  
Yupeng Wang
Keyword(s):  
Anderson Localization ◽  
Topological Superconductor ◽  
Localization Transition ◽  
One Dimensional

scholarly journals Localization transition in weakly interacting Bose superfluids in one-dimensional quasiperdiodic lattices

2014 ◽  
Vol 90 (6) ◽  
Author(s):  
Samuel Lellouch ◽  
Laurent Sanchez-Palencia
Keyword(s):  
Localization Transition ◽  
One Dimensional ◽  
Weakly Interacting

scholarly journals Mobility Edges in One-dimensional Disordered Aharonov-Bohm Rings

2019 ◽  
Vol 29 (4) ◽  
pp. 471
Author(s):  
Phi Ba Nguyen
Keyword(s):  
Tight Binding ◽  
System Size ◽  
Disorder Strength ◽  
Weak Disorder ◽  
Localization Transition ◽  
One Dimensional ◽  
Energy Disorder ◽  
Hamiltonian Model ◽  
Aharonov Bohm ◽  
Flux Energy

We study numerically the localization properties of the eigenstates of a tight-binding Hamiltonian model for noninteracting electrons moving in a one-dimensional disordered ring pierced by an Aharonov-Bohm flux. By analyzing the dependence of the inverse participation ratio on Aharonov-Bohm flux, energy, disorder strength and system size, we find that all states in the ring are delocalized in the weak disorder limit. The states lying deeply in the band tails will undergo a continuous delocalization-localization transition as the disorder strength in the ring sweeps from the weak to the strong disorder regime.

scholarly journals Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems

2017 ◽  
Vol 119 (26) ◽  
Author(s):  
Henrik P. Lüschen ◽  
Pranjal Bordia ◽  
Sebastian Scherg ◽  
Fabien Alet ◽  
Ehud Altman ◽  
...  
Keyword(s):  
Many Body ◽  
Slow Dynamics ◽  
Localization Transition ◽  
One Dimensional ◽  
Quasiperiodic Systems ◽  
The Many

scholarly journals Synthesizing multi-dimensional excitation dynamics and localization transition in one-dimensional lattices

2019 ◽  
Vol 14 (2) ◽  
pp. 76-81 ◽  
Author(s):  
Lukas J. Maczewsky ◽  
Kai Wang ◽  
Alexander A. Dovgiy ◽  
Andrey E. Miroshnichenko ◽  
Alexander Moroz ◽  
...  
Keyword(s):  
Localization Transition ◽  
One Dimensional ◽  
Excitation Dynamics

scholarly journals Theory of the Many-Body Localization Transition in One-Dimensional Systems

2015 ◽  
Vol 5 (3) ◽  
Author(s):  
Ronen Vosk ◽  
David A. Huse ◽  
Ehud Altman
Keyword(s):  
Many Body ◽  
Localization Transition ◽  
One Dimensional ◽  
The Many
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