Matrix model and stationary problem in the Toda chain

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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.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalTheoretical and Mathematical Physics
Volume146
Issue number1
DOIs
Publication statusPublished - Jan 2006
Externally publishedYes

Keywords

  • Complex geometry
  • Integrable systems
  • Matrix models

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