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Eigenvalue Dynamics off the Calogero-Moser system
KTH, Superseded Departments, Mathematics.
KTH, Superseded Departments, Mathematics.
2004 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, no 2, 121-129 p.Article in journal (Refereed) Published
Abstract [en]

By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.

Place, publisher, year, edition, pages
2004. Vol. 68, no 2, 121-129 p.
Keyword [en]
eigenvalue dynamics; symmetric matrix; integrable systems; BODY PROBLEMS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-7899DOI: 10.1023/B:MATH.0000043320.41280.76ISI: 000225322400006OAI: oai:DiVA.org:kth-7899DiVA: diva2:13066
Note
QC 20100630Available from: 2008-01-16 Created: 2008-01-16 Last updated: 2011-11-01Bibliographically approved
In thesis
1. Graph Techniques for Matrix Equations and Eigenvalue Dynamics
Open this publication in new window or tab >>Graph Techniques for Matrix Equations and Eigenvalue Dynamics
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

One way to construct noncommutative analogues of a Riemannian manifold Σ is to make use of the Toeplitz quantization procedure. In Paper III and IV, we construct C-algebras for a continuously deformable class of spheres and tori, and by introducing the directed graph of a representation, we can completely characterize the representation theory of these algebras in terms of the corresponding graphs. It turns out that the irreducible representations are indexed by the periodic orbits and N-strings of an iterated map s:(reals) 2→(reals)2 associated to the algebra. As our construction allows for transitions between spheres and tori (passing through a singular surface), one easily sees how the structure of the matrices changes as the topology changes.

In Paper II, noncommutative analogues of minimal surface and membrane equations are constructed and new solutions are presented -- some of which correspond to minimal tori embedded in S7.

Paper I is concerned with the problem of finding differential equations for the eigenvalues of a symmetric N × N matrix satisfying Xdd=0.

Namely, by finding N(N-1)/2 suitable conserved quantities, the time-evolution of X (with arbitrary initial conditions), is reduced to non-linear equations involving only the eigenvalues of Χ.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. vi, 29 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 08-MA-02
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-4608 (URN)978-91-7178-845-0 (ISBN)
Public defence
2008-02-08, F3, KTH, Lindstedtsvägen 26, Stockholm, 14:00
Opponent
Supervisors
Note
QC 20100630Available from: 2008-01-16 Created: 2008-01-16 Last updated: 2010-07-01Bibliographically approved

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