Infiniteness of the Discrete Spectrum of Two-Particle Discrete Schrödinger Operators
We consider a family of discrete Schrödinger operators where is the two-particle quasi-momentum associated to a system of two particles on the -dimensional lattice . When the pre-image of the two-particle dispersion relation at the right edge of the essential spectrum of is of dimension or , we obta...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2023-07, Vol.44 (7), p.2781-2789 |
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| container_issue | 7 |
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| container_title | Lobachevskii journal of mathematics |
| container_volume | 44 |
| creator | Lakaev, Sh. S. |
| description | We consider a family of discrete Schrödinger operators
where
is the two-particle quasi-momentum associated to a system of two particles on the
-dimensional lattice
. When the pre-image of the two-particle dispersion relation at the right edge
of the essential spectrum of
is of dimension
or
, we obtain the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of
to the right of the essential spectrum, while in the case
, the number of eigenvalues
is finite. |
| doi_str_mv | 10.1134/S1995080223070272 |
| format | Article |
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where
is the two-particle quasi-momentum associated to a system of two particles on the
-dimensional lattice
. When the pre-image of the two-particle dispersion relation at the right edge
of the essential spectrum of
is of dimension
or
, we obtain the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of
to the right of the essential spectrum, while in the case
, the number of eigenvalues
is finite.</description><identifier>ISSN: 1995-0802</identifier><identifier>EISSN: 1818-9962</identifier><identifier>DOI: 10.1134/S1995080223070272</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Algebra ; Analysis ; Eigenvalues ; Geometry ; Mathematical Logic and Foundations ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Probability Theory and Stochastic Processes</subject><ispartof>Lobachevskii journal of mathematics, 2023-07, Vol.44 (7), p.2781-2789</ispartof><rights>Pleiades Publishing, Ltd. 2023</rights><rights>Pleiades Publishing, Ltd. 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-5d3c560c839f3f2275571b2f5e1c5361728e6239358dbe59e0cee7eccf953b243</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1995080223070272$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1995080223070272$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Lakaev, Sh. S.</creatorcontrib><title>Infiniteness of the Discrete Spectrum of Two-Particle Discrete Schrödinger Operators</title><title>Lobachevskii journal of mathematics</title><addtitle>Lobachevskii J Math</addtitle><description>We consider a family of discrete Schrödinger operators
where
is the two-particle quasi-momentum associated to a system of two particles on the
-dimensional lattice
. When the pre-image of the two-particle dispersion relation at the right edge
of the essential spectrum of
is of dimension
or
, we obtain the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of
to the right of the essential spectrum, while in the case
, the number of eigenvalues
is finite.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Eigenvalues</subject><subject>Geometry</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Probability Theory and Stochastic Processes</subject><issn>1995-0802</issn><issn>1818-9962</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kN1Kw0AQhRdRsFYfwLuA19Hd2e5m91LqX6FQoe11SLezNqVN4uwG8cV8AV_MhAoK4tUMnO-cYQ5jl4JfCyFHN3NhreKGA0ieccjgiA2EESa1VsNxt3dy2uun7CyELe9ArfWALSeVL6syYoUhJLVP4gaTuzI4wojJvEEXqd33wuKtTp8LiqXb_Sbchj4_1mX1gpTMGqQi1hTO2YkvdgEvvueQLR_uF-OndDp7nIxvp6kDbWKq1tIpzZ2R1ksPkCmViRV4hcIpqUUGBjVIK5VZr1BZ5A4xQ-e8VXIFIzlkV4fchurXFkPMt3VLVXcyB2OkFBp4T4kD5agOgdDnDZX7gt5zwfO-vfxPe50HDp7Qsf1zP8n_m74A3Vtxaw</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>Lakaev, Sh. S.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230701</creationdate><title>Infiniteness of the Discrete Spectrum of Two-Particle Discrete Schrödinger Operators</title><author>Lakaev, Sh. S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-5d3c560c839f3f2275571b2f5e1c5361728e6239358dbe59e0cee7eccf953b243</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Eigenvalues</topic><topic>Geometry</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Probability Theory and Stochastic Processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lakaev, Sh. S.</creatorcontrib><collection>CrossRef</collection><jtitle>Lobachevskii journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lakaev, Sh. S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Infiniteness of the Discrete Spectrum of Two-Particle Discrete Schrödinger Operators</atitle><jtitle>Lobachevskii journal of mathematics</jtitle><stitle>Lobachevskii J Math</stitle><date>2023-07-01</date><risdate>2023</risdate><volume>44</volume><issue>7</issue><spage>2781</spage><epage>2789</epage><pages>2781-2789</pages><issn>1995-0802</issn><eissn>1818-9962</eissn><abstract>We consider a family of discrete Schrödinger operators
where
is the two-particle quasi-momentum associated to a system of two particles on the
-dimensional lattice
. When the pre-image of the two-particle dispersion relation at the right edge
of the essential spectrum of
is of dimension
or
, we obtain the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of
to the right of the essential spectrum, while in the case
, the number of eigenvalues
is finite.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1995080223070272</doi><tpages>9</tpages></addata></record> |
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| identifier | ISSN: 1995-0802 |
| ispartof | Lobachevskii journal of mathematics, 2023-07, Vol.44 (7), p.2781-2789 |
| issn | 1995-0802 1818-9962 |
| language | eng |
| recordid | cdi_proquest_journals_2883316204 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Eigenvalues Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operators (mathematics) Probability Theory and Stochastic Processes |
| title | Infiniteness of the Discrete Spectrum of Two-Particle Discrete Schrödinger Operators |
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