A New Class of Solvable Many-Body Problems
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A New Class of Solvable Many-Body Problems
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| Creator |
Calogero, F.
Yi, G. |
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| Description |
A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces) featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t) explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections). Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
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| Date |
2019-02-18T12:40:52Z
2019-02-18T12:40:52Z 2012 |
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| Type |
Article
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| Identifier |
A New Class of Solvable Many-Body Problems / F. Calogero, G. Yi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 24 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 70F10; 70H06; 37J35; 37K10 DOI: http://dx.doi.org/10.3842/SIGMA.2012.066 http://dspace.nbuv.gov.ua/handle/123456789/148447 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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