The Well-Known Result: Rigorous or Not?

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In summary, The topic being discussed is the rigor of the result for Anderson localization. It is mentioned that in 1D, the result is fully rigorous and a quick Google search brings up numerous references and papers on the subject. However, there is some skepticism about the rigor of the result compared to Bloch's theorem. It is clarified that the Bloch and Floquet theorems are indeed rigorous.
  • #1
wdlang
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it is a well known result, but it is a rigorious result or not?
 
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  • #2


You mean Anderson localization?
 
  • #3


tom.stoer said:
You mean Anderson localization?

yes.
 
  • #4


In 1D, yes, it is fully rigorous. A quick google brings up references and papers --- too many to list here.
 
  • #5


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.
 
  • #6


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!
 
  • #7


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

1. Is the well-known result always considered to be rigorous?

No, the well-known result may not always be considered rigorous. It depends on the specific situation and context in which the result is being applied.

2. What factors determine if a well-known result is rigorous?

The factors that determine if a well-known result is rigorous include the validity of the assumptions and the soundness of the logical reasoning used to arrive at the result.

3. Can a result be well-known but not rigorous?

Yes, a result can be well-known but not rigorous. This could be due to a lack of evidence or proof to support the result, or because the result has been widely accepted without being thoroughly tested.

4. How important is it for a result to be rigorously proven?

Rigorous proof is essential for a result to be considered valid and reliable. Without rigorous proof, the result may be based on flawed assumptions or faulty reasoning, leading to incorrect conclusions.

5. Do scientists always strive for rigorous results?

Yes, scientists always strive for rigorous results. The scientific method is based on rigorous testing and validation of hypotheses, and scientists are constantly working to improve and refine their methods to ensure the rigor of their results.

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