Midgap spectrum of the fermion-vortex system
I study the midgap spectrum of the fermion-vortex system in two spatial dimensions. The existence of bound states, in addition to the zero modes found by Jackiw and Rossi, is established. For a singly quantized vortex, I present complete analytical solutions in terms of generalized Laguerre polynomi...
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| description | I study the midgap spectrum of the fermion-vortex system in two spatial dimensions. The existence of bound states, in addition to the zero modes found by Jackiw and Rossi, is established. For a singly quantized vortex, I present complete analytical solutions in terms of generalized Laguerre polynomials in the opposite limits of vanishing and large vortex core size. There is an infinite number of such bound states, with a spectrum that is, when squared, given by, respectively, the Coulomb potential and the isotropic harmonic oscillator. Possible experimental signatures of this spectrum in condensed-matter realizations of the system are pointed out. |
| doi_str_mv | 10.48550/arxiv.0807.0618 |
| format | Article |
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The existence of bound states, in addition to the zero modes found by Jackiw and Rossi, is established. For a singly quantized vortex, I present complete analytical solutions in terms of generalized Laguerre polynomials in the opposite limits of vanishing and large vortex core size. There is an infinite number of such bound states, with a spectrum that is, when squared, given by, respectively, the Coulomb potential and the isotropic harmonic oscillator. Possible experimental signatures of this spectrum in condensed-matter realizations of the system are pointed out.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.0807.0618</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Condensed matter physics ; Coulomb potential ; Exact solutions ; Fermions ; Harmonic oscillators ; Mathematical analysis ; Physics - Mesoscale and Nanoscale Physics ; Physics - Strongly Correlated Electrons ; Physics - Superconductivity ; Polynomials ; Vortices</subject><ispartof>arXiv.org, 2008-07</ispartof><rights>2008. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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The existence of bound states, in addition to the zero modes found by Jackiw and Rossi, is established. For a singly quantized vortex, I present complete analytical solutions in terms of generalized Laguerre polynomials in the opposite limits of vanishing and large vortex core size. There is an infinite number of such bound states, with a spectrum that is, when squared, given by, respectively, the Coulomb potential and the isotropic harmonic oscillator. Possible experimental signatures of this spectrum in condensed-matter realizations of the system are pointed out.</description><subject>Condensed matter physics</subject><subject>Coulomb potential</subject><subject>Exact solutions</subject><subject>Fermions</subject><subject>Harmonic oscillators</subject><subject>Mathematical analysis</subject><subject>Physics - Mesoscale and Nanoscale Physics</subject><subject>Physics - Strongly Correlated Electrons</subject><subject>Physics - Superconductivity</subject><subject>Polynomials</subject><subject>Vortices</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj89rwyAYhmUwaOl636kIuy7Zp0ajx1H2Czp26V3U6Jay1EyT0v73S9fBB-_l4X2_B6FbAmUlOYcHk47toQQJdQmCyCs0p4yRQlaUztAy5x0AUFFTztkc3b-3zafpce69G9LY4Rjw8OVx8Klr4744xDT4I86nPPjuBl0H85398j8XaPv8tF2_FpuPl7f146YwnPAiONoEqkINhnvHnJy2lFfAZB0YgFNCUjkRglinwMjpmLWhss5K0ojAFmh1qf0z0X1qO5NO-mykz0YTcHcB-hR_Rp8HvYtj2k8vaQoKRF0B4ewXIzhNeQ</recordid><startdate>20080703</startdate><enddate>20080703</enddate><creator>Seradjeh, B</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>GOX</scope></search><sort><creationdate>20080703</creationdate><title>Midgap spectrum of the fermion-vortex system</title><author>Seradjeh, B</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a515-fc2df29f70a5ec3c86729e90387f300c96828df261bc90a80a83bbf4bcb81d6f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Condensed matter physics</topic><topic>Coulomb potential</topic><topic>Exact solutions</topic><topic>Fermions</topic><topic>Harmonic oscillators</topic><topic>Mathematical analysis</topic><topic>Physics - Mesoscale and Nanoscale Physics</topic><topic>Physics - Strongly Correlated Electrons</topic><topic>Physics - Superconductivity</topic><topic>Polynomials</topic><topic>Vortices</topic><toplevel>online_resources</toplevel><creatorcontrib>Seradjeh, B</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Seradjeh, B</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Midgap spectrum of the fermion-vortex system</atitle><jtitle>arXiv.org</jtitle><date>2008-07-03</date><risdate>2008</risdate><eissn>2331-8422</eissn><abstract>I study the midgap spectrum of the fermion-vortex system in two spatial dimensions. The existence of bound states, in addition to the zero modes found by Jackiw and Rossi, is established. For a singly quantized vortex, I present complete analytical solutions in terms of generalized Laguerre polynomials in the opposite limits of vanishing and large vortex core size. There is an infinite number of such bound states, with a spectrum that is, when squared, given by, respectively, the Coulomb potential and the isotropic harmonic oscillator. Possible experimental signatures of this spectrum in condensed-matter realizations of the system are pointed out.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.0807.0618</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Condensed matter physics Coulomb potential Exact solutions Fermions Harmonic oscillators Mathematical analysis Physics - Mesoscale and Nanoscale Physics Physics - Strongly Correlated Electrons Physics - Superconductivity Polynomials Vortices |
| title | Midgap spectrum of the fermion-vortex system |
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