Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators
<p dir="ltr">In resumming a divergent series, one is frequently confronted with situations where predictions from traditional resummation techniques might not accurate when considering strong-coupling values. Besides, in literature, we barely can find a resummation algorithm for whic...
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2023
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| _version_ | 1864513561237127168 |
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| author | I.S. Elkamash (16810689) |
| author2 | Hamdi M. Abdelhamid (16810692) Abouzeid M. Shalaby (16810695) |
| author2_role | author author |
| author_facet | I.S. Elkamash (16810689) Hamdi M. Abdelhamid (16810692) Abouzeid M. Shalaby (16810695) |
| author_role | author |
| dc.creator.none.fl_str_mv | I.S. Elkamash (16810689) Hamdi M. Abdelhamid (16810692) Abouzeid M. Shalaby (16810695) |
| dc.date.none.fl_str_mv | 2023-10-01T00:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1016/j.aop.2023.169427 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Entire_hypergeometric_approximants_for_the_ground_state_energy_perturbation_series_of_the_quartic_sextic_and_octic_anharmonic_oscillators/24166521 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Physical sciences Classical physics Hypergeometric algorithim Divergent series Large-order behavior Strong coupling behavior |
| dc.title.none.fl_str_mv | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">In resumming a divergent series, one is frequently confronted with situations where predictions from traditional resummation techniques might not accurate when considering strong-coupling values. Besides, in literature, we barely can find a resummation algorithm for which the convergence is faster for stronglydivergent ( Gevrey − k , k > 1) series than a divergent one ( Gevrey − 1 ). In this work, we use appropriate hypergeometric functions to approximate a divergent series ( n! large order growth factor) and strongly-divergent series ( (2n)! and (3n)! large order growth factors). We found that the convergence of the predicted non-perturbative parameters to their exact values is faster for the challenging Gevrey−3 than the Gevrey−2 series which in turn is faster than the divergent Gevrey − 1 series. To explain such interesting feature, we suggest a type of analytic continuation where the parametrized divergent hypergeometric series is represented as a finite sum over entire hypergeometric functions. The algorithm is applied to sum the weak-coupling series of the ground state energy of the quartic (divergent), sextic (Gevrey−2) and Octic (Gevrey−3) anharmonic oscillators. Accurate results are obtained for the ground state energy as well as the predicted non-perturbative parameters. While traditional resummation techniques fail to give reliable results for large coupling values, our algorithm gives the expected limit as the coupling goes to infinity.</p><h2>Other Information</h2><p dir="ltr">Published in: Annals of Physics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aop.2023.169427" target="_blank">https://dx.doi.org/10.1016/j.aop.2023.169427</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_02aa36ada2ff8b9ee36d04b2bc1b888a |
| identifier_str_mv | 10.1016/j.aop.2023.169427 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/24166521 |
| publishDate | 2023 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillatorsI.S. Elkamash (16810689)Hamdi M. Abdelhamid (16810692)Abouzeid M. Shalaby (16810695)Physical sciencesClassical physicsHypergeometric algorithimDivergent seriesLarge-order behaviorStrong coupling behavior<p dir="ltr">In resumming a divergent series, one is frequently confronted with situations where predictions from traditional resummation techniques might not accurate when considering strong-coupling values. Besides, in literature, we barely can find a resummation algorithm for which the convergence is faster for stronglydivergent ( Gevrey − k , k > 1) series than a divergent one ( Gevrey − 1 ). In this work, we use appropriate hypergeometric functions to approximate a divergent series ( n! large order growth factor) and strongly-divergent series ( (2n)! and (3n)! large order growth factors). We found that the convergence of the predicted non-perturbative parameters to their exact values is faster for the challenging Gevrey−3 than the Gevrey−2 series which in turn is faster than the divergent Gevrey − 1 series. To explain such interesting feature, we suggest a type of analytic continuation where the parametrized divergent hypergeometric series is represented as a finite sum over entire hypergeometric functions. The algorithm is applied to sum the weak-coupling series of the ground state energy of the quartic (divergent), sextic (Gevrey−2) and Octic (Gevrey−3) anharmonic oscillators. Accurate results are obtained for the ground state energy as well as the predicted non-perturbative parameters. While traditional resummation techniques fail to give reliable results for large coupling values, our algorithm gives the expected limit as the coupling goes to infinity.</p><h2>Other Information</h2><p dir="ltr">Published in: Annals of Physics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aop.2023.169427" target="_blank">https://dx.doi.org/10.1016/j.aop.2023.169427</a></p>2023-10-01T00:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.aop.2023.169427https://figshare.com/articles/journal_contribution/Entire_hypergeometric_approximants_for_the_ground_state_energy_perturbation_series_of_the_quartic_sextic_and_octic_anharmonic_oscillators/24166521CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/241665212023-10-01T00:00:00Z |
| spellingShingle | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators I.S. Elkamash (16810689) Physical sciences Classical physics Hypergeometric algorithim Divergent series Large-order behavior Strong coupling behavior |
| status_str | publishedVersion |
| title | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| title_full | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| title_fullStr | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| title_full_unstemmed | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| title_short | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| title_sort | Entire hypergeometric approximants for the ground state energy perturbation series of the quartic, sextic and octic anharmonic oscillators |
| topic | Physical sciences Classical physics Hypergeometric algorithim Divergent series Large-order behavior Strong coupling behavior |