About: Almost Mathieu operator

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In mathematical physics, the almost Mathieu operator arises in the study of the quantum Hall effect. It is given by acting as a self-adjoint operator on the Hilbert space . Here are parameters. In pure mathematics, its importance comes from the fact of being one of the best-understood examples of an ergodic Schrödinger operator. For example, three problems (now all solved) of Barry Simon's fifteen problems about Schrödinger operators "for the twenty-first century" featured the almost Mathieu operator. In physics, the almost Mathieu operators can be used to study metal to insulator transitions like in the Aubry–André model.

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rdfs:label	Almost Mathieu operator (en) 概マシュー作用素 (ja)
rdfs:comment	数理物理学の分野における概マシュー作用素（がいマシューさようそ、英: almost Mathieu operator）とは、量子ホール効果の研究に現れる、次のような作用素のことを言う。この作用素はヒルベルト空間上で自己共役作用素として働く。ここではパラメータである。純粋数学の分野では、この作用素の重要性は、なシュレーディンガー作用素のよく知られた例であるという事実に起因する。例えば、（今ではすべて解かれた）シュレーディンガー作用素に関するバリー・サイモンの「21世紀のための」15の問題は、概マシュー作用素を取り上げたものであった。に対して、概マシュー作用素はしばしばハーパーの方程式（Harper's equation）と呼ばれる。 (ja) In mathematical physics, the almost Mathieu operator arises in the study of the quantum Hall effect. It is given by acting as a self-adjoint operator on the Hilbert space . Here are parameters. In pure mathematics, its importance comes from the fact of being one of the best-understood examples of an ergodic Schrödinger operator. For example, three problems (now all solved) of Barry Simon's fifteen problems about Schrödinger operators "for the twenty-first century" featured the almost Mathieu operator. In physics, the almost Mathieu operators can be used to study metal to insulator transitions like in the Aubry–André model. (en)
foaf:depiction
dcterms:subject	Spectral theory Mathematical physics
Wikipage page ID	16628707 (xsd:integer)
Wikipage revision ID	1117924689 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum Hall effect Michael Herman (mathematician) Barry Simon Spectral theory Anderson localization Spectrum (functional analysis) Mathematical physics Irrational number Lebesgue measure Ergodic Absolutely continuous Floquet theory Aubry–André model Jean Bourgain Artur Avila Mathematical physics Svetlana Jitomirskaya Hofstadter's butterfly Douglas Hofstadter Cantor set Rational number Self-adjoint operator Lyapunov exponent Pure mathematics Schrödinger operator
sameAs	Almost Mathieu operator Almost Mathieu operator Almost Mathieu operator Almost Mathieu operator
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description dbt:Functional_analysis
thumbnail	wiki-commons:Special:FilePath/Hofstadter's_butterfly.png?width=300
has abstract	In mathematical physics, the almost Mathieu operator arises in the study of the quantum Hall effect. It is given by acting as a self-adjoint operator on the Hilbert space . Here are parameters. In pure mathematics, its importance comes from the fact of being one of the best-understood examples of an ergodic Schrödinger operator. For example, three problems (now all solved) of Barry Simon's fifteen problems about Schrödinger operators "for the twenty-first century" featured the almost Mathieu operator. In physics, the almost Mathieu operators can be used to study metal to insulator transitions like in the Aubry–André model. For , the almost Mathieu operator is sometimes called Harper's equation. (en) 数理物理学の分野における概マシュー作用素（がいマシューさようそ、英: almost Mathieu operator）とは、量子ホール効果の研究に現れる、次のような作用素のことを言う。この作用素はヒルベルト空間上で自己共役作用素として働く。ここではパラメータである。純粋数学の分野では、この作用素の重要性は、なシュレーディンガー作用素のよく知られた例であるという事実に起因する。例えば、（今ではすべて解かれた）シュレーディンガー作用素に関するバリー・サイモンの「21世紀のための」15の問題は、概マシュー作用素を取り上げたものであった。に対して、概マシュー作用素はしばしばハーパーの方程式（Harper's equation）と呼ばれる。 (ja)
prov:wasDerivedFrom	wikipedia-en:Almost_Mathieu_operator?oldid=1117924689&ns=0
page length (characters) of wiki page	8816 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Almost_Mathieu_operator
is Link from a Wikipage to another Wikipage of	Decomposition of spectrum (functional analysis) Ruth Lyttle Satter Prize in Mathematics Almost Mathieu Operator Almost mathieu operator Simon problems Aubry–André model Artur Avila Hofstadter's butterfly Ten Martini Problem Ten martini problem
is Wikipage redirect of	Almost Mathieu Operator Almost mathieu operator Ten Martini Problem Ten martini problem
is foaf:primaryTopic of	wikipedia-en:Almost_Mathieu_operator

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