Geodesic
The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master $T$-operator for the quantum inhomogeneous ${\rm GL}(N)$ $XXX$ spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master $T$-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars–Schneider system of particles.
Keywords: quantum integrable spin chains; classical many-body systems; quantum-classical correspondence; master $T$-operator; tau-function. 
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     author = {Anton Zabrodin},
     title = {The {Master} $T${-Operator} for {Inhomogeneous} $XXX$ {Spin} {Chain} and {mKP} {Hierarchy}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a5/}
}
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Anton Zabrodin. The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a5/

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