On the invariant method for the time-dependent non-Hermitian Hamiltonians
. We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators H ( t ) that generate a real phase in their time evolution. This involves the use of invariant operators I P H ( t ) that are pseudo-Hermitian with respect to the time-dependent metric operator, which impli...
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| Veröffentlicht in: | European physical journal plus 2017-06, Vol.132 (6), p.258, Article 258 |
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| creator | Khantoul, B. Bounames, A. Maamache, M. |
| description | .
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators
H
(
t
) that generate a real phase in their time evolution. This involves the use of invariant operators
I
P
H
(
t
)
that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore,
H
(
t
) is generally not quasi-Hermitian and does not define an observable of the system but
I
P
H
(
t
)
obeys a quasi-Hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example. |
| doi_str_mv | 10.1140/epjp/i2017-11524-7 |
| format | Article |
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We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators
H
(
t
) that generate a real phase in their time evolution. This involves the use of invariant operators
I
P
H
(
t
)
that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore,
H
(
t
) is generally not quasi-Hermitian and does not define an observable of the system but
I
P
H
(
t
)
obeys a quasi-Hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2017-11524-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Atomic ; Complex Systems ; Condensed Matter Physics ; Eigenvalues ; Evolution ; Hamiltonian functions ; Harmonic oscillators ; Invariants ; Mathematical and Computational Physics ; Molecular ; Operators ; Optical and Plasma Physics ; Physics ; Physics and Astronomy ; Quantum physics ; Regular Article ; Symmetry ; Theoretical ; Time dependence</subject><ispartof>European physical journal plus, 2017-06, Vol.132 (6), p.258, Article 258</ispartof><rights>Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017</rights><rights>Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-4c7aa0aa71eaadf0e7d2c5d1e0e9c0a19341e3f1a07e7f034c3a67165b1b3623</citedby><cites>FETCH-LOGICAL-c319t-4c7aa0aa71eaadf0e7d2c5d1e0e9c0a19341e3f1a07e7f034c3a67165b1b3623</cites><orcidid>0000-0002-5998-2710</orcidid></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/i2017-11524-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919505763?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Khantoul, B.</creatorcontrib><creatorcontrib>Bounames, A.</creatorcontrib><creatorcontrib>Maamache, M.</creatorcontrib><title>On the invariant method for the time-dependent non-Hermitian Hamiltonians</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators
H
(
t
) that generate a real phase in their time evolution. This involves the use of invariant operators
I
P
H
(
t
)
that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore,
H
(
t
) is generally not quasi-Hermitian and does not define an observable of the system but
I
P
H
(
t
)
obeys a quasi-Hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Eigenvalues</subject><subject>Evolution</subject><subject>Hamiltonian functions</subject><subject>Harmonic oscillators</subject><subject>Invariants</subject><subject>Mathematical and Computational Physics</subject><subject>Molecular</subject><subject>Operators</subject><subject>Optical and Plasma Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum physics</subject><subject>Regular Article</subject><subject>Symmetry</subject><subject>Theoretical</subject><subject>Time dependence</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kE1LAzEQhoMoWGr_gKcFz7GZJLshRylqhUIvvYd0d9amdJM1SQX_vWkr6Mm5zMD7MfAQcg_sEUCyOY77ce44A0UBai6puiITDprRWkp5_ee-JbOU9qyM1CC1nJC3ta_yDivnP2101udqwLwLXdWHeBayG5B2OKLvsKg-eLrEOLhczNXSDu6Qgy93uiM3vT0knP3sKdm8PG8WS7pav74tnla0FaAzla2yllmrAK3teoaq423dATLULbOghQQUPVimUPVMyFbYRkFTb2ErGi6m5OFSO8bwccSUzT4coy8fDdega1arRhQXv7jaGFKK2JsxusHGLwPMnKCZEzRzhmbO0IwqIXEJpWL27xh_q_9JfQPDunGY</recordid><startdate>20170601</startdate><enddate>20170601</enddate><creator>Khantoul, B.</creator><creator>Bounames, A.</creator><creator>Maamache, M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</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><orcidid>https://orcid.org/0000-0002-5998-2710</orcidid></search><sort><creationdate>20170601</creationdate><title>On the invariant method for the time-dependent non-Hermitian Hamiltonians</title><author>Khantoul, B. ; Bounames, A. ; Maamache, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-4c7aa0aa71eaadf0e7d2c5d1e0e9c0a19341e3f1a07e7f034c3a67165b1b3623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Eigenvalues</topic><topic>Evolution</topic><topic>Hamiltonian functions</topic><topic>Harmonic oscillators</topic><topic>Invariants</topic><topic>Mathematical and Computational Physics</topic><topic>Molecular</topic><topic>Operators</topic><topic>Optical and Plasma Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum physics</topic><topic>Regular Article</topic><topic>Symmetry</topic><topic>Theoretical</topic><topic>Time dependence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Khantoul, B.</creatorcontrib><creatorcontrib>Bounames, A.</creatorcontrib><creatorcontrib>Maamache, M.</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><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khantoul, B.</au><au>Bounames, A.</au><au>Maamache, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the invariant method for the time-dependent non-Hermitian Hamiltonians</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2017-06-01</date><risdate>2017</risdate><volume>132</volume><issue>6</issue><spage>258</spage><pages>258-</pages><artnum>258</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>.
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators
H
(
t
) that generate a real phase in their time evolution. This involves the use of invariant operators
I
P
H
(
t
)
that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore,
H
(
t
) is generally not quasi-Hermitian and does not define an observable of the system but
I
P
H
(
t
)
obeys a quasi-Hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2017-11524-7</doi><orcidid>https://orcid.org/0000-0002-5998-2710</orcidid></addata></record> |
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| ispartof | European physical journal plus, 2017-06, Vol.132 (6), p.258, Article 258 |
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| language | eng |
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| source | Springer Online Journals Complete; ProQuest Central UK/Ireland; ProQuest Central |
| subjects | Applied and Technical Physics Atomic Complex Systems Condensed Matter Physics Eigenvalues Evolution Hamiltonian functions Harmonic oscillators Invariants Mathematical and Computational Physics Molecular Operators Optical and Plasma Physics Physics Physics and Astronomy Quantum physics Regular Article Symmetry Theoretical Time dependence |
| title | On the invariant method for the time-dependent non-Hermitian Hamiltonians |
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