Geodesic
Matrix Model and Stationary Problem in the Toda Chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 3-16

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2006_146_1_a0,
     author = {A. V. Marshakov},
     title = {Matrix {Model} and {Stationary} {Problem} in the {Toda} {Chain}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {146},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a0/}
}
TY  - JOUR
AU  - A. V. Marshakov
TI  - Matrix Model and Stationary Problem in the Toda Chain
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 3
EP  - 16
VL  - 146
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a0/
LA  - ru
ID  - TMF_2006_146_1_a0
ER  - 
%0 Journal Article
%A A. V. Marshakov
%T Matrix Model and Stationary Problem in the Toda Chain
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 3-16
%V 146
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a0/
%G ru
%F TMF_2006_146_1_a0
A. V. Marshakov. Matrix Model and Stationary Problem in the Toda Chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a0/