Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions
We analyze the thermodynamics of the focusing discrete nonlinear Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$ and under a model with two parameters, representing inverse temperature and strength of the nonlinearity, respectively. We prove the existence of lim...
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| creator | Dey, Partha S Kirkpatrick, Kay Krishnan, Kesav |
| description | We analyze the thermodynamics of the focusing discrete nonlinear
Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$
and under a model with two parameters, representing inverse temperature and
strength of the nonlinearity, respectively. We prove the existence of limiting
free energy and analyze the phase diagram for general $d,p$. We also prove the
existence of a continuous phase transition curve that divides the parametric
plane into two regions involving the appearance or non-appearance of solitons.
Appropriate upper and lower bounds for the curve are constructed. We also look
at the typical behavior of a function chosen from the Gibbs measure for certain
parts of the phase diagram. |
| doi_str_mv | 10.48550/arxiv.2212.00276 |
| format | Article |
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Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$
and under a model with two parameters, representing inverse temperature and
strength of the nonlinearity, respectively. We prove the existence of limiting
free energy and analyze the phase diagram for general $d,p$. We also prove the
existence of a continuous phase transition curve that divides the parametric
plane into two regions involving the appearance or non-appearance of solitons.
Appropriate upper and lower bounds for the curve are constructed. We also look
at the typical behavior of a function chosen from the Gibbs measure for certain
parts of the phase diagram.</description><identifier>DOI: 10.48550/arxiv.2212.00276</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Mathematical Physics ; Mathematics - Probability ; Physics - Mathematical Physics</subject><creationdate>2022-11</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2212.00276$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2212.00276$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dey, Partha S</creatorcontrib><creatorcontrib>Kirkpatrick, Kay</creatorcontrib><creatorcontrib>Krishnan, Kesav</creatorcontrib><title>Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions</title><description>We analyze the thermodynamics of the focusing discrete nonlinear
Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$
and under a model with two parameters, representing inverse temperature and
strength of the nonlinearity, respectively. We prove the existence of limiting
free energy and analyze the phase diagram for general $d,p$. We also prove the
existence of a continuous phase transition curve that divides the parametric
plane into two regions involving the appearance or non-appearance of solitons.
Appropriate upper and lower bounds for the curve are constructed. We also look
at the typical behavior of a function chosen from the Gibbs measure for certain
parts of the phase diagram.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Probability</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjrEKwkAQRK-xEPUDrFzsjZfTqL1GUogIphTDkWxyC-aie1H0702CvdXA8GZ4Qox96S03QSDnmt_08pTylSelWq_64noy2iHErK2jmioLecWwI5cy1gjHpjiQRc1wTg1fplVGtkCG8PHUHU4WYsOIoG0GERUG23mJzV1l3VD0cn1zOPrlQEz2YbyNZp1JcmcqNX-S1ijpjBb_iS-AxkEe</recordid><startdate>20221130</startdate><enddate>20221130</enddate><creator>Dey, Partha S</creator><creator>Kirkpatrick, Kay</creator><creator>Krishnan, Kesav</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20221130</creationdate><title>Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions</title><author>Dey, Partha S ; Kirkpatrick, Kay ; Krishnan, Kesav</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2212_002763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Probability</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Dey, Partha S</creatorcontrib><creatorcontrib>Kirkpatrick, Kay</creatorcontrib><creatorcontrib>Krishnan, Kesav</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dey, Partha S</au><au>Kirkpatrick, Kay</au><au>Krishnan, Kesav</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions</atitle><date>2022-11-30</date><risdate>2022</risdate><abstract>We analyze the thermodynamics of the focusing discrete nonlinear
Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$
and under a model with two parameters, representing inverse temperature and
strength of the nonlinearity, respectively. We prove the existence of limiting
free energy and analyze the phase diagram for general $d,p$. We also prove the
existence of a continuous phase transition curve that divides the parametric
plane into two regions involving the appearance or non-appearance of solitons.
Appropriate upper and lower bounds for the curve are constructed. We also look
at the typical behavior of a function chosen from the Gibbs measure for certain
parts of the phase diagram.</abstract><doi>10.48550/arxiv.2212.00276</doi><oa>free_for_read</oa></addata></record> |
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| title | Phase Transition for Discrete Non Linear Schr\"odinger Equation in Three and Higher Dimensions |
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