The GGE averaged currents of the classical Toda chain

Cao, Xiangyu; Bulchandani, Vir B.; Spohn, Herbert

doi:10.1088/1751-8121/ab5019

Cited by 27 publications

(23 citation statements)

References 29 publications

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“…Regarding the spin current in the XXZ model the same formula was proven in [4]. The currents were also investigated in the classical Toda chain in [5]. Finally, in [6] the author and two collaborators derived an exact finite volume result for the current mean values, valid in a large class of Bethe Ansatz solvable quantum models.…”

Section: Introductionmentioning

confidence: 78%

Current operators in integrable spin chains: lessons from long range deformations

Pozsgay

2020

SciPost Phys.

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We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU (3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.

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Section: Introductionmentioning

confidence: 78%

Current operators in integrable spin chains: lessons from long range deformations

Pozsgay

2020

SciPost Phys.

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“…The holographic dual of the classical GGE state discussed in this paper is the KdV analog of the GGE for another classical integrable model recently discussed in [39,40]. The next logical step here would be to develop a theory of generalized hydrodynamics describing long-wave dynamics of states locally deviating from the GGE [41][42][43][44][45].…”

Section: Discussionmentioning

confidence: 96%

KdV-charged black holes

Dymarsky

Sugishita

2020

J. High Energ. Phys.

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We construct black hole geometries in AdS 3 with non-trivial values of KdV charges. The black holes are holographically dual to quantum KdV Generalized Gibbs Ensemble in 2d CFT. They satisfy thermodynamic identity and thus are saddle point configurations of the Euclidean gravity path integral. We discuss holographic calculation of the KdV generalized partition function and show that for a certain value of chemical potentials new geometries, not the conventional BTZ ones, are the leading saddles.

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“…Linear-response theory deals with the response of a system to an additional perturbation in the Hamiltonian. It sprouted up from studies conducted in the 1950s that connected equilibrium correlation functions and nonequilibrium properties, leading to the fluctuation-dissipation relation obtained by (Callen and Welton, 1951) and to Green-Kubo type formulae for transport coefficients obtained in (Green, 1952(Green, , 1954 and (Kubo, 1957) [for an early review, see (Zwanzig, 1965)].…”

Section: A Frameworkmentioning

confidence: 99%