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Diffusive or balistic? Spread of the wave packet when localized and extended states coexist

If the lattice is perfectly periodic, then the wave packet of a particle initially located on a site spreads balistically. Namely, its size increases linearly in time. Now, introduce disorder into ...
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55 views

Inuitive analogy for localization?

I'm looking for a plain English analogy for electron/wave localization. And in particular weak localization and Anderson/strong localization. Is it possible to describe these phenomena in simple terms ...
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64 views

Is interaction a relevant perturbation for 1d Anderson localization of fermions?

Disorder is a relevant perturbation in 1d, which drives the system to Anderson localization. My question is if I am already at the Anderson localization fixed point, how to analyze the scaling ...
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139 views

scaling theory of Anderson localization

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$ His question was whether the eigenstates ...
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0answers
57 views

How to derive Eq.(1) in Prof. A Leggett's lecture note?

I came across a lecture note on weak localisation by Prof. A. J. Leggett. In this note, he wrote down his first equation as follows: $$\sigma = \lim_{\omega\rightarrow 0} \lim_{q\rightarrow 0} \frac{1}...
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1answer
732 views

What is many body localization?

Is there any good definition of many body localization? It is the property of one state or it is the property of a Hamiltonian? Why does disorder play an important role in many body localization? ...
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2answers
495 views

What is Anderson localization? Could someone give an example worked out in detail?

What is Anderson localization, for someone with no previous knowledge on the subject? I tried to read Anderson's original paper, but it was too terse for me. I have seen a couple of intuitive ...
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3answers
2k views

Introduction to Anderson localization

I find Anderson's original paper too terse. I am looking for something that introduces me gently to the subject so that I can understand Anderson's paper and other literature. What references are out ...