Spectral problem for the mean field Hamiltonian
We consider the mean field Hamiltonian HV = κ ΔV + ξ(·) in l2(V ), where V = {x} is a finite set. Characteristic equations for eigenvalues and expressions for eigenfunctions of HV are obtained. Using this result, the spectral representation of the solution of the corresponding ("head transition...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2021-06-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/24252 |
| _version_ | 1811285181756080128 |
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| author | Arvydas Astrauskas |
| author_facet | Arvydas Astrauskas |
| author_sort | Arvydas Astrauskas |
| collection | DOAJ |
| description | We consider the mean field Hamiltonian HV = κ ΔV + ξ(·) in l2(V ), where V = {x} is a finite set. Characteristic equations for eigenvalues and expressions for eigenfunctions of HV are obtained. Using this result, the spectral representation of the solution of the corresponding ("head transition'') differential equation is derived. |
| first_indexed | 2024-04-13T02:40:34Z |
| format | Article |
| id | doaj.art-8b4ed0ca05db48a6b738461d5bd764d5 |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-04-13T02:40:34Z |
| publishDate | 2021-06-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-8b4ed0ca05db48a6b738461d5bd764d52022-12-22T03:06:14ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2021-06-0147spec.10.15388/LMR.2007.24252Spectral problem for the mean field HamiltonianArvydas Astrauskas0Institute of Mathematics and InformaticsWe consider the mean field Hamiltonian HV = κ ΔV + ξ(·) in l2(V ), where V = {x} is a finite set. Characteristic equations for eigenvalues and expressions for eigenfunctions of HV are obtained. Using this result, the spectral representation of the solution of the corresponding ("head transition'') differential equation is derived.https://www.journals.vu.lt/LMR/article/view/24252mean field difference operatoreigenvalue problemcharacteristic equation for eigenvalueslinear differential equationsspectral representation of solutions |
| spellingShingle | Arvydas Astrauskas Spectral problem for the mean field Hamiltonian Lietuvos Matematikos Rinkinys mean field difference operator eigenvalue problem characteristic equation for eigenvalues linear differential equations spectral representation of solutions |
| title | Spectral problem for the mean field Hamiltonian |
| title_full | Spectral problem for the mean field Hamiltonian |
| title_fullStr | Spectral problem for the mean field Hamiltonian |
| title_full_unstemmed | Spectral problem for the mean field Hamiltonian |
| title_short | Spectral problem for the mean field Hamiltonian |
| title_sort | spectral problem for the mean field hamiltonian |
| topic | mean field difference operator eigenvalue problem characteristic equation for eigenvalues linear differential equations spectral representation of solutions |
| url | https://www.journals.vu.lt/LMR/article/view/24252 |
| work_keys_str_mv | AT arvydasastrauskas spectralproblemforthemeanfieldhamiltonian |