Analytical solution of the classical Bethe-ansatz equation for the Toda chain

1985 ◽  
Vol 112 (5) ◽  
pp. 201-203 ◽  
Author(s):  
M. Opper
Keyword(s):  
Analytical Solution ◽  
Bethe Ansatz ◽  
Toda Chain

scholarly journals Quantum relativistic Toda chain at root of unity: isospectrality, modifiedQ-operator, and functional Bethe ansatz

2002 ◽  
Vol 31 (9) ◽  
pp. 513-553 ◽  
Author(s):  
Stanislav Pakuliak ◽  
Sergei Sergeev
Keyword(s):  
Bethe Ansatz ◽  
Weyl Algebra ◽  
Separation Of Variables ◽  
Toda Chain ◽  
Special Choice ◽  
Finite Dimensional Representation ◽  
Classical Counterpart ◽  
Discrete Integrable System ◽  
Root Of Unity ◽  
Finite Dimensional

We investigate anN-state spin model called quantum relativistic Toda chain and based on the unitary finite-dimensional representations of the Weyl algebra withqbeingNth primitive root of unity. Parameters of the finite-dimensional representation of the local Weyl algebra form the classical discrete integrable system. Nontrivial dynamics of the classical counterpart corresponds to isospectral transformations of the spin system. Similarity operators are constructed with the help of modified Baxter'sQ-operators. The classical counterpart of the modifiedQ-operator for the initial homogeneous spin chain is a Bäcklund transformation. This transformation creates an extra Hirota-type soliton in a parameterization of the chain structure. Special choice of values of solitonic amplitudes yields a degeneration of spin eigenstates, leading to the quantum separation of variables, or the functional Bethe ansatz. A projector to the separated eigenstates is constructed explicitly as a product of modifiedQ-operators.

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

THE CN TODA CHAIN

1994 ◽  
Vol 08 (04) ◽  
pp. 475-486
Author(s):  
V. Pasquier
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Toda Chain ◽  
Exact Equation

We obtain the exact equation for the spectrum of the CN Toda chain and for a spin chain which gives the Toda chain back in the infinite spin limit. The method we use is a variant of the Bethe Ansatz technique discovered by Sklyanin based on M. Gutzwiller's solution of the AN case.

THERMODYNAMICS OF THE TODA CHAIN

1994 ◽  
Vol 08 (18) ◽  
pp. 2391-2446 ◽  
Author(s):  
ALESSANDRO CUCCOLI ◽  
ROBERTO LIVI ◽  
MAURO SPICCI ◽  
VALERIO TOGNETTI ◽  
RUGGERO VAIA
Keyword(s):  
Bethe Ansatz ◽  
Equations Of Motion ◽  
Classical System ◽  
Toda Chain ◽  
Integral Approach ◽  
Transform Method ◽  
Static Correlation ◽  
Dynamical Features ◽  
Quantum Thermodynamic ◽  
Made In

A review of the classical and quantum thermodynamic properties of the Toda chain is provided, together with a survey of the techniques that have been used to work them out, i.e., the bilateral Laplace transform method for the classical system, the Bethe–Ansatz and the variational path-integral approach for the quantum one. For the classical Toda chain we also recall some of the main dynamical features, i.e. the integrability of the model and the soliton-like solutions of the equations of motion. In the quantum case a comparison between the Bethe–Ansatz and the variational method is made. In particular it is shown as the latter offers the possibility of also evaluating static correlation functions.

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