The Well-Known Result: Rigorous or Not?

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Discussion Overview

The discussion centers around the rigor of the result known as Anderson localization, particularly in one-dimensional systems. Participants explore whether this result is established as rigorous in the context of theoretical physics, referencing related concepts such as Bloch's theorem and Floquet theory.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that Anderson localization in one dimension is fully rigorous, citing numerous references and papers.
  • Others challenge this assertion, questioning the rigor of Anderson localization by comparing it to Bloch's theorem, which they believe is not rigorously dealt with.
  • One participant defends the rigor of Bloch's theorem, stating it is indeed rigorous.
  • Another participant expresses the view that both Bloch and Floquet theorems are rigorous, suggesting a broader context for the discussion of rigor.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the rigor of Anderson localization, with competing views on the rigor of both Anderson localization and Bloch's theorem being expressed.

wdlang
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it is a well known result, but it is a rigorious result or not?
 
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You mean Anderson localization?
 


tom.stoer said:
You mean Anderson localization?

yes.
 


In 1D, yes, it is fully rigorous. A quick google brings up references and papers --- too many to list here.
 


genneth said:
In 1D, yes, it is fully rigorous. A quick google brings up references and papers --- too many to list here.

I don't believe this. Even the Bloch's theorem is not dealt with rigorously, so how could the Anderson localization then? The Anderson localization looks like more complicated phenomenon than Bloch waves.
 


jostpuur said:
I don't believe this. Even the Bloch's theorem is not dealt with rigorously, so how could the Anderson localization then? The Anderson localization looks like more complicated phenomenon than Bloch waves.

no, bloch theorem is rigorious!
 


Afaik the Bloch and the (more general) Floquet theorems are rigorous.
 

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