Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map
We show that for any doubling map generated C 1 monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by log λ - C for all energies, where C depends only on the potential. In particular, it ans...
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| Veröffentlicht in: | Communications in mathematical physics 2024-10, Vol.405 (10), Article 231 |
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| container_title | Communications in mathematical physics |
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| creator | Zhang, Zhenghe |
| description | We show that for any doubling map generated
C
1
monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by
log
λ
-
C
for all energies, where
C
depends only on the potential. In particular, it answers an open question [
D
, Problem 5] raised by D. Damanik. |
| doi_str_mv | 10.1007/s00220-024-05109-0 |
| format | Article |
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C
1
monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by
log
λ
-
C
for all energies, where
C
depends only on the potential. In particular, it answers an open question [
D
, Problem 5] raised by D. Damanik.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-024-05109-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical and Quantum Gravitation ; Complex Systems ; Liapunov exponents ; Mathematical and Computational Physics ; Mathematical Physics ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Schrodinger equation ; Theoretical</subject><ispartof>Communications in mathematical physics, 2024-10, Vol.405 (10), Article 231</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c244t-110ccae3e626e198b70531551496caaa1a9724e9f455104e6791a4aa711324223</cites><orcidid>0000-0001-5942-3110</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00220-024-05109-0$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00220-024-05109-0$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Zhang, Zhenghe</creatorcontrib><title>Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We show that for any doubling map generated
C
1
monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by
log
λ
-
C
for all energies, where
C
depends only on the potential. In particular, it answers an open question [
D
, Problem 5] raised by D. Damanik.</description><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Liapunov exponents</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Schrodinger equation</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMFKAzEQhoMoWKsv4CngeXUmm802R6m1Ci16sOeQrtm6pU3WJFvctzd1BW-ehhm-7x_4CblGuEWA8i4AMAYZMJ5BgSAzOCEj5DnLQKI4JSMAhCwXKM7JRQhbAJBMiBHRK9vUzu_pqwtNbA5N7KmrafwwdNHrtrPuQGdfrbPGRppAunTWxbQmIaZbo3eBzo01XkfzTtf9j_rguvWusRu61O0lOasTZK5-55isHmdv06ds8TJ_nt4vsopxHjNEqCptciOYMCgn6xKKHIsCuRSV1hq1LBk3subpBtyIUqLmWpeIOeOM5WNyM-S23n12JkS1dZ236aXKkzABIRESxQaq8i4Eb2rV-mavfa8Q1LFKNVSpUpXqp0p1lPJBCgm2G-P_ov-xvgFFv3Wq</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Zhang, Zhenghe</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5942-3110</orcidid></search><sort><creationdate>20241001</creationdate><title>Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map</title><author>Zhang, Zhenghe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-110ccae3e626e198b70531551496caaa1a9724e9f455104e6791a4aa711324223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Liapunov exponents</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Schrodinger equation</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Zhenghe</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Zhenghe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>405</volume><issue>10</issue><artnum>231</artnum><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>We show that for any doubling map generated
C
1
monotone potential with derivative uniformly bounded away from zero and infinity, the Lyapunov exponent of the associated Schrödinger operators is bounded below by
log
λ
-
C
for all energies, where
C
depends only on the potential. In particular, it answers an open question [
D
, Problem 5] raised by D. Damanik.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-024-05109-0</doi><orcidid>https://orcid.org/0000-0001-5942-3110</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Classical and Quantum Gravitation Complex Systems Liapunov exponents Mathematical and Computational Physics Mathematical Physics Operators (mathematics) Physics Physics and Astronomy Quantum Physics Relativity Theory Schrodinger equation Theoretical |
| title | Uniform Positivity of the Lyapunov Exponent for Monotone Potentials Generated by the Doubling Map |
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