Almost Mathieu operator: Difference between revisions

Revision as of 07:58, 16 February 2024

Revision as of 04:23, 19 February 2024

Line 1:

{{Short description|Self-adjoint operator that arises in physical transition problems}}

In [[mathematical physics]], the '''almost Mathieu operator''', named for its similarity to the [[Mathieu function|Mathieu operator]]<ref name=simon1982almost>{{cite journal |last1=Simon |first1=Barry |year=1982 |title=Almost periodic Schrodinger operators: a review |journal=Advances in Applied Mathematics |volume=3 |issue=4 |pages=463-490}}</ref> introduced by [[Émile Léonard Mathieu]],<ref>{{cite web |title=Mathieu equation |url=https://encyclopediaofmath.org/wiki/Mathieu_equation |website=Encyclopedia of Mathematics |publisher=Springer |access-date=February 9, 2024}}</ref>, arises in the study of the [[quantum Hall effect]]. It is given by

: <math> [H^{\lambda,\alpha}_\omega u](n) = u(n+1) + u(n-1) + 2 \lambda \cos(2\pi (\omega + n\alpha)) u(n), \, </math>

Line 14:

}}

This problem was named the 'Dry Ten Martini Problem' by [[Barry Simon]] as it was [[Martini (cocktail)#Preparation|'stronger']] than the weaker problem which became known as the 'Ten Martini Problem':<ref name=simon1982almost></ref>:

{{blockquote|text=