Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation
. In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic...
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| Veröffentlicht in: | European physical journal plus 2016-07, Vol.131 (7), p.220, Article 220 |
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| creator | Reinisch, Gilbert C. Gazeau, Maxime |
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In this paper we consider a basic two-level
nonlinear
quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant
is provided within 99.95% accuracy by the present first-order
non-relativistic
and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested). |
| doi_str_mv | 10.1140/epjp/i2016-16220-6 |
| format | Article |
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In this paper we consider a basic two-level
nonlinear
quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant
is provided within 99.95% accuracy by the present first-order
non-relativistic
and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2016-16220-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Atomic ; Complex Systems ; Condensed Matter Physics ; Eigenvectors ; Fine structure ; Ground state ; Hamiltonian functions ; Helium ; Mathematical and Computational Physics ; Molecular ; Nonlinear Sciences ; Nonlinearity ; Optical and Plasma Physics ; Orthogonality ; Physics ; Physics and Astronomy ; Poisson equation ; Quantum dots ; Quantum electrodynamics ; Quantum mechanics ; Regular Article ; Theoretical</subject><ispartof>European physical journal plus, 2016-07, Vol.131 (7), p.220, Article 220</ispartof><rights>Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016</rights><rights>Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c353t-5320e82a402505317664239fed26062fbdd229c862561c21ca3ff279259226e93</citedby><cites>FETCH-LOGICAL-c353t-5320e82a402505317664239fed26062fbdd229c862561c21ca3ff279259226e93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/i2016-16220-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919718837?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>230,314,780,784,885,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03476263$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Reinisch, Gilbert C.</creatorcontrib><creatorcontrib>Gazeau, Maxime</creatorcontrib><title>Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
In this paper we consider a basic two-level
nonlinear
quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant
is provided within 99.95% accuracy by the present first-order
non-relativistic
and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Eigenvectors</subject><subject>Fine structure</subject><subject>Ground state</subject><subject>Hamiltonian functions</subject><subject>Helium</subject><subject>Mathematical and Computational Physics</subject><subject>Molecular</subject><subject>Nonlinear Sciences</subject><subject>Nonlinearity</subject><subject>Optical and Plasma Physics</subject><subject>Orthogonality</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Poisson equation</subject><subject>Quantum dots</subject><subject>Quantum electrodynamics</subject><subject>Quantum mechanics</subject><subject>Regular Article</subject><subject>Theoretical</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kU1O3DAYhiMEEgi4QFeWuuoijP3ZccbdIVo6SCO1Arq2jPOF8Sixg51BmpNwk16gF6tDKuiq3vhHz_vY8lsUHxi9YEzQBQ7bYeGAMlkyCUBLeVCcAFO0rIQQh_-sj4vzlLY0D6GYUOKkeLkNHZLQEh985zya6MY9cX7alyuMvRud8eRpZ_y460mPdmO8s-kz-YLJRjeMLvgpP4ffQOzQjjE0e2_6jJM2hp6MG3y_h9zZTfz9q3H-EWP5I7iUsgmzYFKeFUet6RKe_51Pi5_XX--vVuX6-7ebq8t1aXnFx7LiQHEJRlCoaMVZLaUArlpsQFIJ7UPTACi7lFBJZoFZw9sWagWVApCo-GnxafZuTKeH6HoT9zoYp1eXaz2dUS5qCZI_s8x-nNkhhqcdplFvwy76_DwNiqmaLZe8zhTMlI0hpYjtm5ZRPfWlp770a1_6tS8tc4jPoZTh6UPe1f9J_QE4Fpyn</recordid><startdate>20160701</startdate><enddate>20160701</enddate><creator>Reinisch, Gilbert C.</creator><creator>Gazeau, Maxime</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>1XC</scope></search><sort><creationdate>20160701</creationdate><title>Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation</title><author>Reinisch, Gilbert C. ; Gazeau, Maxime</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-5320e82a402505317664239fed26062fbdd229c862561c21ca3ff279259226e93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Eigenvectors</topic><topic>Fine structure</topic><topic>Ground state</topic><topic>Hamiltonian functions</topic><topic>Helium</topic><topic>Mathematical and Computational Physics</topic><topic>Molecular</topic><topic>Nonlinear Sciences</topic><topic>Nonlinearity</topic><topic>Optical and Plasma Physics</topic><topic>Orthogonality</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Poisson equation</topic><topic>Quantum dots</topic><topic>Quantum electrodynamics</topic><topic>Quantum mechanics</topic><topic>Regular Article</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Reinisch, Gilbert C.</creatorcontrib><creatorcontrib>Gazeau, Maxime</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science 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>Hyper Article en Ligne (HAL)</collection><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Reinisch, Gilbert C.</au><au>Gazeau, Maxime</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2016-07-01</date><risdate>2016</risdate><volume>131</volume><issue>7</issue><spage>220</spage><pages>220-</pages><artnum>220</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>.
In this paper we consider a basic two-level
nonlinear
quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant
is provided within 99.95% accuracy by the present first-order
non-relativistic
and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2016-16220-6</doi></addata></record> |
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| subjects | Applied and Technical Physics Atomic Complex Systems Condensed Matter Physics Eigenvectors Fine structure Ground state Hamiltonian functions Helium Mathematical and Computational Physics Molecular Nonlinear Sciences Nonlinearity Optical and Plasma Physics Orthogonality Physics Physics and Astronomy Poisson equation Quantum dots Quantum electrodynamics Quantum mechanics Regular Article Theoretical |
| title | Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation |
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