Questions tagged [anderson-localization]
An insulated state in a non-interacting system arising from the destructive interference among multiple-scattering paths in a condensed matter system.
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Anderson localization in the continuum case
I haven't looked into Anderson localization before. A quick review of the available information gives the impression that this phenomenon has mainly been studied for the case of a discrete random ...
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Critical disorder strength for anderson model (for a discrete system) [closed]
I have written the hopping matrix of a lattice in real space (in real space because i have disorder in the system and hence bloch theory is not valid). On-site disorder has been introduced through a ...
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Anderson localization
Numerically how we can show that states are localized for strong disorder? If I make a 3D plot of E vs IPR vs Disorder and show that for a particular value of disorder, where the IPR is approaching 1 ...
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How to exactly diagonalize a system with $Z_2\times Z_2$ symmetry?
I am studying the localization protected SPT phase, and try to compute the level spacing ratio of Hamiltonian,
$$H=\sum_kJ_kZ_{k-1}X_kZ_{k+1}+\sum_kh_kX_{k}X_{k+1}.$$
We can check that this ...
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Inverse participation ratio (IPR) literature
I am curently working with the inverse participation ratio (IPR) as a measure of localization but I can't find literature that just explains why and how exactly it relates to localization. I get the ...
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(Anderson Localization)Time evolution of occupation number of free fermion model
I encounter a difficulty in comouting the time evolution of occupation number. I want to compute the time evolution of occupation number of Aubry-Andre model to show that there exists Anderson ...
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Experimental detection of Anderson localization of light in 3D vs 2D
I have a question about the experimental realization of Anderson localization of light. I am a theorist, and have not worked much in optics, so please bear with me.
Anderson localization of light in ...
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Scale invariance beyond the critical point
Using Anderson localization as an example, I understand how scale invariance comes into play at a critical point - at a critical point, the localization length $\xi$ (the average "radius" of ...
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Phase transition vs. critical phenomena
Just trying to get some clarity in terminology: is phase transitions synonymous with critical phenomena? At the first glance they mean the same thing, but I am not sure whether phase transitions ...
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What is the meaning or definition of 'correlation length' in the context of Anderson localization?
I was reading a paper that talks about Anderson localization. It mentions the quantity called 'correlation length' or 'localization length' but no formal definition is given as to what it actually ...
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Proof that the self-energy is an inverse lifetime
My question concerns the self-energy of a diagonal propagator for a single-particle lattice problem. The context is Anderson Localisation, but really it's a problem of complex analysis. I would like ...
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Does Anderson localisation occur if the potential are equal in pairs?
Consider the Anderson model given by the Hamiltonian $H \in B(l^2( \mathbb{Z}^d)) $ defined by $H = - \Delta + V$ where the potential $V$ acts on a unit vector $ \vert x \rangle \in l^2( \mathbb{Z}^d)...
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What is the meaning of Thouless energy?
Wikipedia article says "a measure of the sensitivity of energy levels to a change in the boundary conditions of the system", which I don't really understand.
Thouless energy is defined as
$$...
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Weak localization, strong localization, and localization without a metal-insulator transition
As I begin to read literature on Anderson localization by disorder, authors are distinguishing between cases that are unfamiliar to me, namely weak localization, strong localization, and localization ...
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Divergences in resolvent expansion of Anderson hamiltonian
I'm reading these lecture notes on Anderson localization, and I cannot understand how the resonant regions contribute to the divergence of the resolvent expansion (sections 3.1 and 3.2). The relevant ...
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