scholarly journals RIGGED CONFIGURATIONS AND THE BETHE ANSATZ

2003 ◽  
Author(s):  
ANNE SCHILLING
Keyword(s):  
Bethe Ansatz ◽  
Rigged Configurations

scholarly journals COMBINATORIAL BETHE ANSATZ AND GENERALIZED PERIODIC BOX-BALL SYSTEM

2008 ◽  
Vol 20 (05) ◽  
pp. 493-527 ◽  
Author(s):  
ATSUO KUNIBA ◽  
REIHO SAKAMOTO
Keyword(s):  
Energy Distribution ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Theta Function ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Local Energy ◽  
Initial Value ◽  
Rigged Configurations ◽  
Higher Spin

We reformulate the Kerov–Kirillov–Reshetikhin (KKR) map in the combinatorial Bethe ansatz from paths to rigged configurations by introducing local energy distribution in crystal base theory. Combined with an earlier result on the inverse map, it completes the crystal interpretation of the KKR bijection for [Formula: see text]. As an application, we solve an integrable cellular automaton, a higher spin generalization of the periodic box-ball system, by an inverse scattering method and obtain the solution of the initial value problem in terms of the ultradiscrete Riemann theta function.

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

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