scholarly journals Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain

Nonlinearity ◽  
2005 ◽  
Vol 18 (6) ◽  
pp. 2795-2813 ◽  
Author(s):  
J A Foxman ◽  
J M Robbins
Keyword(s):  
Toda Chain ◽  
Periodic Toda Chain

Lecture on SUSY Gauge Theories and Integrable Systems

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3093-3124
Author(s):  
A. Marshakov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Toda Chain ◽  
Quantum Field ◽  
Standard Quantum ◽  
Integrable Equations ◽  
Complex Curves ◽  
Periodic Toda Chain

I consider main features of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential. The example of periodic Toda chain solutions is considered in detail. Recently found exact nonperturbative solutions to [Formula: see text] SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to the integrable systems are discussed.

Chaos upon soliton decay in a perturbed periodic toda chain

1986 ◽  
Vol 23 (1-3) ◽  
pp. 374-380 ◽  
Author(s):  
Karlheinz Geist ◽  
Werner Lauterborn
Keyword(s):  
Toda Chain ◽  
Perturbed Periodic ◽  
Periodic Toda Chain

scholarly journals Quantization conditions for the periodic Toda chain: Inadequacy of Bethe-ansatz methods

1989 ◽  
Vol 39 (16) ◽  
pp. 11800-11809 ◽  
Author(s):  
Michael Fowler ◽  
Holger Frahm
Keyword(s):  
Bethe Ansatz ◽  
Toda Chain ◽  
Periodic Toda Chain

Semiclassical quantization of the periodic Toda chain

1993 ◽  
Vol 26 (24) ◽  
pp. 7589-7613 ◽  
Author(s):  
F Gohmann ◽  
W Pesch ◽  
F G Mertens
Keyword(s):  
Toda Chain ◽  
Semiclassical Quantization ◽  
Periodic Toda Chain

scholarly journals Quantum relativistic Toda chain

2001 ◽  
Vol 1 (2) ◽  
pp. 47-68 ◽  
Author(s):  
G. Pronko ◽  
Sergei Sergeev
Keyword(s):  
Unit Circle ◽  
Weyl Algebra ◽  
Toda Chain ◽  
Periodic Toda Chain

Investigated is the quantum relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl’sqwe are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six-vertexR-matrix. Both independent Baxter’sQ-operators are constructed explicitly as seria over local Weyl generators. The operator-valued Wronskian ofR-matrix. Both independent Baxter’sQsis also calculated.

scholarly journals Adiabatic Invariants for the FPUT and Toda Chain in the Thermodynamic Limit

2020 ◽  
Vol 380 (2) ◽  
pp. 811-851
Author(s):  
T. Grava ◽  
A. Maspero ◽  
G. Mazzuca ◽  
A. Ponno
Keyword(s):  
Periodic Boundary ◽  
Toda Chain ◽  
Periodic Boundary Conditions ◽  
Adiabatic Invariants ◽  
Hamiltonian Flow ◽  
Integrals Of Motion ◽  
Linear Combinations ◽  
Small Temperature ◽  
Large Measure ◽  
Periodic Toda Chain

Abstract We consider the Fermi–Pasta–Ulam–Tsingou (FPUT) chain composed by $$N \gg 1$$ N ≫ 1 particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $$\beta ^{-1}$$ β - 1 . Given a fixed $${1\le m \ll N}$$ 1 ≤ m ≪ N , we prove that the first m integrals of motion of the periodic Toda chain are adiabatic invariants of FPUT (namely they are approximately constant along the Hamiltonian flow of the FPUT) for times of order $$\beta $$ β , for initial data in a set of large measure. We also prove that special linear combinations of the harmonic energies are adiabatic invariants of the FPUT on the same time scale, whereas they become adiabatic invariants for all times for the Toda dynamics.

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