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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 146, Number 1, Pages 3–16
DOI: https://doi.org/10.4213/tmf2004 (Mi tmf2004) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Matrix Model and Stationary Problem in the Toda Chain

A. V. Marshakovab

a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Full-text PDF (187 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf2004
Abstract: We analyze the stationary problem for the Toda chain and show that the arising geometric data exactly correspond to the multisupport solutions of the one-matrix model with a polynomial potential. We calculate the Hamiltonians and symplectic forms for the first nontrivial examples explicitly and perform the consistency checks. We formulate the corresponding quantum problem and discuss some of its properties and prospects.
Keywords: matrix models, complex geometry, integrable systems.
English version:
Theoretical and Mathematical Physics, 2006, Volume 146, Issue 1, Pages 1–12
DOI: https://doi.org/10.1007/s11232-006-0001-0
Bibliographic databases:
Language: Russian
Citation: A. V. Marshakov, “Matrix Model and Stationary Problem in the Toda Chain”, TMF, 146:1 (2006), 3–16; Theoret. and Math. Phys., 146:1 (2006), 1–12
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf2004
  • https://doi.org/10.4213/tmf2004
  • https://www.mathnet.ru/eng/tmf/v146/i1/p3
    • This publication is cited in the following 2 articles:
    1. Marshakov, AV, “Matrix models, complex geometry, and integrable systems: II”, Theoretical and Mathematical Physics, 147:3 (2006), 777  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. A. V. Marshakov, “Matrix models, complex geometry, and integrable systems: II∗”, Theoret. and Math. Phys., 147:3 (2006), 777–820  mathnet  mathnet  crossref  crossref  isi  scopus
    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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    References:91
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