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Generalized Adiabatic Invariance
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| Zeitschriftentitel: | Journal of Mathematical Physics |
|---|---|
| Personen und Körperschaften: | |
| In: | Journal of Mathematical Physics, 5, 1964, 3, S. 355-362 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
AIP Publishing
|
| Schlagwörter: |
| author_facet |
Garrido, L. M. Garrido, L. M. |
|---|---|
| author |
Garrido, L. M. |
| spellingShingle |
Garrido, L. M. Journal of Mathematical Physics Generalized Adiabatic Invariance Mathematical Physics Statistical and Nonlinear Physics |
| author_sort |
garrido, l. m. |
| spelling |
Garrido, L. M. 0022-2488 1089-7658 AIP Publishing Mathematical Physics Statistical and Nonlinear Physics http://dx.doi.org/10.1063/1.1704127 <jats:p>In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m − 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).</jats:p> Generalized Adiabatic Invariance Journal of Mathematical Physics |
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10.1063/1.1704127 |
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Online |
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Mathematik Physik |
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AIP Publishing, 1964 |
| imprint_str_mv |
AIP Publishing, 1964 |
| issn |
0022-2488 1089-7658 |
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0022-2488 1089-7658 |
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English |
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garrido1964generalizedadiabaticinvariance |
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1964 |
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AIP Publishing |
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ai |
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Journal of Mathematical Physics |
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49 |
| title |
Generalized Adiabatic Invariance |
| title_unstemmed |
Generalized Adiabatic Invariance |
| title_full |
Generalized Adiabatic Invariance |
| title_fullStr |
Generalized Adiabatic Invariance |
| title_full_unstemmed |
Generalized Adiabatic Invariance |
| title_short |
Generalized Adiabatic Invariance |
| title_sort |
generalized adiabatic invariance |
| topic |
Mathematical Physics Statistical and Nonlinear Physics |
| url |
http://dx.doi.org/10.1063/1.1704127 |
| publishDate |
1964 |
| physical |
355-362 |
| description |
<jats:p>In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m − 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).</jats:p> |
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| author | Garrido, L. M. |
| author_facet | Garrido, L. M., Garrido, L. M. |
| author_sort | garrido, l. m. |
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| container_start_page | 355 |
| container_title | Journal of Mathematical Physics |
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| description | <jats:p>In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m − 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).</jats:p> |
| doi_str_mv | 10.1063/1.1704127 |
| facet_avail | Online |
| finc_class_facet | Mathematik, Physik |
| format | ElectronicArticle |
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| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA2My8xLjE3MDQxMjc |
| imprint | AIP Publishing, 1964 |
| imprint_str_mv | AIP Publishing, 1964 |
| institution | DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-D161, DE-Gla1, DE-Zi4, DE-15 |
| issn | 0022-2488, 1089-7658 |
| issn_str_mv | 0022-2488, 1089-7658 |
| language | English |
| last_indexed | 2024-03-01T18:01:49.459Z |
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| mega_collection | AIP Publishing (CrossRef) |
| physical | 355-362 |
| publishDate | 1964 |
| publishDateSort | 1964 |
| publisher | AIP Publishing |
| record_format | ai |
| recordtype | ai |
| series | Journal of Mathematical Physics |
| source_id | 49 |
| spelling | Garrido, L. M. 0022-2488 1089-7658 AIP Publishing Mathematical Physics Statistical and Nonlinear Physics http://dx.doi.org/10.1063/1.1704127 <jats:p>In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m − 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).</jats:p> Generalized Adiabatic Invariance Journal of Mathematical Physics |
| spellingShingle | Garrido, L. M., Journal of Mathematical Physics, Generalized Adiabatic Invariance, Mathematical Physics, Statistical and Nonlinear Physics |
| title | Generalized Adiabatic Invariance |
| title_full | Generalized Adiabatic Invariance |
| title_fullStr | Generalized Adiabatic Invariance |
| title_full_unstemmed | Generalized Adiabatic Invariance |
| title_short | Generalized Adiabatic Invariance |
| title_sort | generalized adiabatic invariance |
| title_unstemmed | Generalized Adiabatic Invariance |
| topic | Mathematical Physics, Statistical and Nonlinear Physics |
| url | http://dx.doi.org/10.1063/1.1704127 |