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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 2, Pages 198–223
DOI: https://doi.org/10.4213/tmf6942
(Mi tmf6942)
 

This article is cited in 6 scientific papers (total in 6 papers)

On a technique to identify solvable discrete-time many-body problems

F. Calogeroab

a Physics Department, University of Rome "La Sapienza", Romе, Italy
b Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Romе, Italy
Full-text PDF (539 kB) Citations (6)
References:
Abstract: The starting point is an $N{\times}N$ matrix, $U\equiv U(\ell)$, evolving in the discrete-time independent variable $\ell=0,1,2,\dots$ according to a solvable matrix evolution equation. One then focuses on the evolution of its $N$ eigenvalues $z_n(\ell)$. This evolution generally also involves $N(N{-}1)$ additional variables. In some cases via a compatible ansatz these additional variables can be expressed in terms of the $N$ variables $z_n(\ell)$. Thereby one obtains a system of discrete-time evolution equations involving only the $N$ dependent variables $z_n(\ell)$, which is often interpretable as a discrete-time many-body problem. Various peculiarities of this approach are investigated, including the possibility to manufacture nontrivial isochronous models (all solutions of which are periodic with the same period). These properties are illustrated via specific examples. In the process novel discrete-time many-body problems are exhibited.
Keywords: integrable discrete-time dynamical system, solvable discrete-time dynamical system, integrable discrete-time many-body problem, solvable discrete-time many-body problem, isochronous discrete-time evolution.
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 2, Pages 1052–1072
DOI: https://doi.org/10.1007/s11232-012-0095-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: F. Calogero, “On a technique to identify solvable discrete-time many-body problems”, TMF, 172:2 (2012), 198–223; Theoret. and Math. Phys., 172:2 (2012), 1052–1072
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6942
  • https://doi.org/10.4213/tmf6942
  • https://www.mathnet.ru/eng/tmf/v172/i2/p198
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:413
    Full-text PDF :194
    References:53
    First page:23
     
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