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Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality.
P. Mazur, Non-ergodicity of phase functions in certain systems , Physica 43
1969
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N. G. Van Kampen, Note on ergodic functions , Physica 53
1971
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M. Suzuki, Ergodicity, constants of motion, and bounds for susceptibilities , Physica 51
1971
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The Toda lattice. II: Existence of Integrals ,
H. Flaschka, · 1974
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Integrals of the Toda lattice ,
M. Henon, · 1974
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Theory of Nonlinear Lattices
M. Toda, · 1989
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X. Zotos, F. Naef, and P. Prelovsek, Transport and conservation laws , Phys. Rev. B 55
1997
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X. Zotos, Ballistic transport in classical and quantum integrable systems, Journal of low temperature physics 126
2002
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B. S. Shastry and A. P. Young, Dynamics of energy transport in a Toda ring , Phys Rev. B 82
2010
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T. Prosen, Open XXZ Spin Chain: Nonequilibrium Steady State and a Strict Bound on Ballistic Transport , Phys. Rev. Lett. 106
2011
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J. Sirker, R. G. Pereira, and I. Affleck, Conservation laws, integrability, and transport in one-dimensional quantum systems , Phys. Rev. B 83
2011
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E. Ilievski and T. Prosen, Thermodyamic bounds on Drude weights in terms of almost-conserved quantities , Commun. Math. Phys. 318
2013
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B. Doyon and H. Spohn, Drude weight for the Lieb-Liniger Bose gas , SciPost Physics 3
2017
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Drude weight for the Lieb-Liniger bose gas ,
B. Doyon and H. Spohn, · 2017
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Interacting and noninteracting integrable systems,
H. Spohn, · 2018
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Generalised hydrodynamics of the classical Toda system ,
B. Doyon, · 2019
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Generalized Gibbs ensembles of the classical Toda chain ,
H. Spohn, · 2019
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The GGE averaged currents of the classical Toda chain ,
X. Cao, V. B. Bulchandani, and H. Spohn, · 2019
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T. Prosen and B. Žunkovič, Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System , Phys. Rev. Lett. 111
2013
Cited alongside, same era.
E. Ilievski and J. De Nardis, Microscopic Origin of Ideal Conductivity in Integrable Quantum Models , PRL 119
2017
Cited alongside, same era.
Quantitative impact of integrals of motion on the eigenstate thermalization hypothesis ,
M. Mierzejewski and L. Vidmar, · 2020
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