Fetching the paper…
Reading the bibliography…
1.
J.W. Gibbs, Elementary Principles in Statistical Mechanics. Charles Scribner’s Sons, 1902
1902
Earlier work this paper cites.
M.S. Green, Markoff random processes and and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids. J. Chem. Phys. 22
1954
Earlier work this paper cites.
C.B. Morrey, On the derivation of hydrodynamics from statistical mechanics, Comm. Pure Appl. Math. 8
1955
Earlier work this paper cites.
F.J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys. 3
1962
Earlier work this paper cites.
E.H. Lieb, Exact analysis of an interacting Bose gas. II. The excitation spectrum, Phys. Rev. 130
1963
Earlier work this paper cites.
E.H. Lieb and W. Liniger, Exact analysis of an interacting Bose gas. I. The general solution and the ground state, Phys. Rev. 130
1963
Earlier work this paper cites.
M. Toda, Vibration of a chain with nonlinear interaction, J. Phys. Soc. Japan 22
1967
Earlier work this paper cites.
M. Toda, Wave propagation in anharmonic lattices, J. Phys. Soc. Japan 23
1967
Earlier work this paper cites.
J.L. Lebowitz, J.K. Percus, and J. Sykes, Time evolution of the total distribution function of a one-dimensional system of hard rods, Phys. Rev. 171
1968
Earlier work this paper cites.
P. Mazur, Non-ergodicity of phase functions in certain systems, Physica 43
1969
Earlier work this paper cites.
J. K. Percus, Exact solutions of kinetics of a model classical fluid, Phys. Fluids 8
1969
Earlier work this paper cites.
D. Ruelle, Statistical Mechanics. Benjamin, Reading MA,1969
1969
Earlier work this paper cites.
C.N. Yang and C.P. Yang, Thermodynamics of a one-dimensional system of Bosons with repulsive delta-function interaction, J. Math. Phys. 10
1969
Earlier work this paper cites.
V. E. Zakharov, Kinetic equation for solitons, Sov. Phys. JETP 33
1971
Earlier work this paper cites.
J. Ford, S.D. Stoddard, and J.S. Turner, On the integrability of the Toda lattice, Progr. Theor. Phys. 50
1973
Earlier work this paper cites.
O.E. Lanford, Entropy and equilibrium states in classical statistical mechanics. In: Statistical Mechanics and Mathematical Problems, ed. by A. Lenard, pp. 1 – 113. Lecture Notes in Physics Vol. 2, Springer Berlin, 1973
1973
Earlier work this paper cites.
R.L. Dobrushin, Conditions for the absence of phase transitions in one-dimensional classical systems, Math. USSR Sb. 22
1974
Earlier work this paper cites.
H. Flaschka, The Toda lattice. II. Existence of integrals, Phys. Rev. B 9
1974
Earlier work this paper cites.
M. Hénon, Integrals of the Toda lattice, Phys. Rev. B 9
1974
Earlier work this paper cites.
E.D.G. Cohen, Fundamental Problems in Statistical Mechanics III, Proceedings of the 1974 Wageningen Summer School. North-Holland, 1975
1975
Earlier work this paper cites.
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions. Benjamin, Reading MA, 1975
1975
Earlier work this paper cites.
L.D. Landau and E.M. Lifshitz, Course in Theoretical Physics, Vol. 6, Fluid Dynamics. Pergamon Press, Oxford (1975)
1975
Earlier work this paper cites.
S.V. Manakov, Complete integrability and stochastization of discrete dynamical systems, Zh. Eksp. Ter. Fiz. 67
1975
Earlier work this paper cites.
J. Moser, Finitely many mass points on the line under the influence of an exponential potential – an integrable system, Dynamical Systems, Theory and Applications, Lecture Note in Physics Vol. 38, pp. 467 – 497. Springer Verlag, 1975
1975
Earlier work this paper cites.
H. Flaschka and D.W. McLaughlin, Canonically conjugate variables for the Korteweg-de Vries equation and the Toda lattice with periodic boundary conditions, Progr. Theor. Phys. 55
1976
Earlier work this paper cites.
P.C. Hohenberg and P.I. Halperin, Theory of dynamical critical phenomena, Rev. Mod. Phys. 49
1977
Earlier work this paper cites.
O.E. Lanford, J.L. Lebowitz, and H. Lieb, Time evolution of infinite anharmonic systems, J. Stat. Phys. 16
1977
Earlier work this paper cites.
H. Spohn and J. L. Lebowitz, Stationary non-equilibrium states of infinite harmonic systems, Commun. Math. Phys. 54
1977
Earlier work this paper cites.
M. Reed and B. Simon, Methods of Modern Mathematical Physics Vol. 4: Analysis of Operators. New York, Academic Press 1978
1978
Earlier work this paper cites.
B. Sutherland, A brief history of the quantum soliton with new results on the quantization of the Toda lattice, Rocky Mountain J. Math. 8
1978
Earlier work this paper cites.
S.C. Oxford, The hamiltonian of the quantized non-linear Schrödinger equation, Ph.D. thesis, UC Los Angeles (1979)
1979
Earlier work this paper cites.
T. Schneider and E. Stoll, Excitation spectrum of the Toda lattice: a molecular-dynamics study, Phys. Rev. Lett. 45
1980
Earlier work this paper cites.
S. Diederich, A conventional approach to dynamic correlations in the Toda lattice, Phys. Lett. A 85
1981
Earlier work this paper cites.
M.C. Gutzwiller, The quantum mechanical Toda lattice, Ann. Phys. 124
1981
Earlier work this paper cites.
W.E. Ferguson, H. Flaschka, and D.W. McLaughlin, Normal modes for the Toda chain, J. Comput. Phys. 45
1982
Earlier work this paper cites.
H. Spohn, Hydrodynamical theory for equilibrium time correlation functions of hard rods, Ann. Phys. (USA) 141
1982
Earlier work this paper cites.
C. Boldrighini, R.L. Dobrushin, and Yu. M. Sukhov, One-dimensional hard rod caricature of hydrodynamics, J. Stat. Phys. 31
1983
Earlier work this paper cites.
M.A. Olshanetsky and A.M.Perelomov, Quantum integrable systems related to Lie algebras, Physics Reports 94
1983
Earlier work this paper cites.
T. Schneider, Classical statistical mechanics of lattice dynamic model systems: transfer integral and molecular-dynamics studies. In: Statics and Dynamics of Nonlinear Systems, eds.: G. Benedek, H.Bilz, R. Zeyher, p. 212 –241. Proceedings Ettore Majorana Centre, Erice, Italy, 1983
1983
Earlier work this paper cites.
N. Theodorakopoulos and F.G. Mertens, Dynamics of the Toda lattice: a soliton-phonon phase-shift analysis, Phys. Rev. B 28
1983
Earlier work this paper cites.
F.G. Mertens, Bethe Ansatz for the Toda lattice: ground state and excitations, Z. Physik B 55
1984
Earlier work this paper cites.
N. Theodorakopoulos, Finite-temperature excitations of the classical Toda chain, Phys. Rev. Lett. 53
1984
Earlier work this paper cites.
M. Opper, Analytical solution of the classical Bethe-ansatz solution for the Toda chain, Phys. Lett. A 112
1985
Earlier work this paper cites.
E.K. Sklyanin, The quantum Toda chain, in: Nonlinear Equations in Classical and Quantum Field Theory, ed. N. Sanchez, pp. 196 – 233, Lecture Notes in Physics, Vol. 226. Springer 1985
1985
Earlier work this paper cites.
M. Hader and F.G. Mertens, Thermodynamics of the Toda lattice, J. Phys. A 19
1986
Earlier work this paper cites.
H. Takayama and M. Ishikawa, Classical thermodynamics of the Toda lattice as a classical limit of the two-component Bethe ansatz scheme, Progr. Theor. Phys. 76
1986
Earlier work this paper cites.
H. Spohn, Interacting Brownian particles: a study of Dyson’s model, in: Hydrodynamic Behavior of Interacting Particle Systems IMA Volumes in Mathematics and its Applications 9, ed. G. Papanicolaou. Springer-Verlag, Berlin, 1987
1987
Earlier work this paper cites.
P. Gruner-Bauer and F.G. Mertens, Excitation spectrum of the Toda lattice for finite temperatures, Z. Physik B, Cond. Mat. 80
1988
Earlier work this paper cites.
R.L. Dobrushin, Caricatures of hydrodynamics, In: IXth International Congress on Mathematical Physics, eds. B. Simon, A. Truman, I.M. Davies, pp. 117 – 132. Adam Hilger, Bristol, 1989
1989
Earlier work this paper cites.
T.C. Dorlas, J.T. Lewis, and J.V. Pulé, The Yang-Yang thermodynamic formalism and large deviations, Comm. Math. Phys. 124
1989
Earlier work this paper cites.
M. Toda, Theory of Nonlinear Lattices, 2nd edition. Springer-Verlag, 1989
1989
Earlier work this paper cites.
D. Takahashi and J. Satsuma, A Soliton Cellular Automaton, J. Phys. Soc. Jpn. 59(10), 3514 (1990)
1990
Earlier work this paper cites.
H. Spohn, Large Scale Dynamics of Interacting Particles. Springer-Verlag, Heidelberg, 1991
1991
Earlier work this paper cites.
S. Venakides, P. Deift, and R. Oba, The Toda shock problem, Comm. Pure Appl. Math. 44
1991
Earlier work this paper cites.
M. Gaudin and V. Pasquier, The periodic Toda chain and a matrix generalization of the Bessel function recursion relations, J. Phys. A 25
1992
Earlier work this paper cites.
A. Cuccoli, M. Spicci, V. Tognetti, and R. Vaia, Dynamic correlations of the classical and quantum Toda lattices, Phys. Rev. B 47
1993
Earlier work this paper cites.
T.C. Dorlas, Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schrödinger model, Comm. Math. Phys. 154
1993
Cited alongside, same era.
S. Olla, S.R.S. Varadhan, and H.-T. Yau, Hydrodynamical limit for a Hamiltonian system with weak noise, Comm. Math. Phys. 155
1993
Cited alongside, same era.
M.P. Grabowski and P. Mathieu, Quantum integrals of motion for the Heisenberg spin chain, Mod. Phys, Lett. A 09
1994
Cited alongside, same era.
H. Castella, X. Zotos, and P. Prelovs̆ek, Integrability and ideal conductance at finite temperatures, Phys. Rev. Lett. 74
1995
Cited alongside, same era.
M.P. Grabowski and P. Mathieu, Structure of the conservation laws in quantum integrable spin chains with short range interactions, Annals of Physics 243
1995
Cited alongside, same era.
J. Quastel and H. Spohn, The one-dimensional KPZ equation and its universality class, J. Stat. Phys. 160
2015
Later among the works it cites.
N. Rougerie, De Finetti Theorems, Mean-Field Limits and Bose-Einstein Condensation, Lecture Notes. Collège de France 2014 and LMU München 2015, arXiv
2015
Later among the works it cites.
D. Bernard and B. Doyon, Conformal field theory out of equilibrium: a review, J. Stat. Mech. 2016
2016
Later among the works it cites.
B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Transport in out-of-equilibrium XXZ chains: exact profiles of charges and currents, Phys. Rev. Lett. 117
2016
Later among the works it cites.
P. Calabrese, F. Essler, and G. Mussardo, Quantum Integrability in Out-of-Equilibrium Systems, special issue, J. Stat. 2016
2016
Later among the works it cites.
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B. Sutherland, Confirmation of the asymptotic Bethe ansatz, Phys. Rev. Lett. 75
1995
Cited alongside, same era.
L.D. Fadeev, How the algebraic Bethe ansatz works for integrable model, arXiv:hep-th/9605187 (1996)
1996
Cited alongside, same era.
C. Boldrighini and Yu. M. Suhov, One-dimensional hard rod caricature of hydrodynamics: Navier-Stokes correction for locally-equilibrium initial states, Commun. Math. Phys. 189
1997
Cited alongside, same era.
E. Cépa and D. Lépingle, Diffusing particles with electrostatic repulsion, Probab. Theory Rel. Fields 107
1997
Cited alongside, same era.
R. Siddharthan and B.S. Shastry, Quantizing the Toda lattice, Phys. Rev. B 55
1997
Cited alongside, same era.
S. Karchev and D. Lebedev, Integral representation for the eigenfunctions of the quantum periodic Toda chain, Lett. Math. Phys. 50
1999
Cited alongside, same era.
M. Takahashi, Thermodynamics of One-Dimensional Solvable Models. Cambridge University Press, Cambridge, 1999
1999
Cited alongside, same era.
F. Carbone, D. Dutykh, and G.A. El, Macroscopic dynamics of incoherent soliton ensembles: Soliton gas kinetics and direct numerical modelling, Europhys. Lett. 113
2016
Later among the works it cites.
O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Emergent hydrodynamics in integrable quantum systems out of equilibrium, Phys. Rev. X 6
2016
Later among the works it cites.
A. Kundu and A. Dhar, Equilibrium dynamical correlations in the Toda chain and other integrable models, Phys. Rev. E 94
2016
Later among the works it cites.
C. Mendl and H. Spohn, Searching for the Tracy-Widom distribution in nonequilibrium processes, Phys. Rev. E 93
2016
Later among the works it cites.
R. Vasseur and J. E. Moore, Nonequilibrium quantum dynamics and transport: from integrability to many-body localization, J. Stat. Mech. 2016
2016
Later among the works it cites.
L. Vidmar and M. Rigol, Generalized Gibbs ensemble in integrable lattice models, J. Stat. Mech. 2016
2016
Later among the works it cites.
V. Alba and P. Calabrese, Entanglement and thermodynamics after a quantum quench in integrable systems, PNAS 114
2017
Later among the works it cites.
V. Bulchandani, R. Vasseur, C. Karrasch, and J.E. Moore, Solvable hydrodynamics of quantum integrable systems, Phys. Rev. Lett. 119
2017
Later among the works it cites.
B. Doyon and H. Spohn, Drude weight for the Lieb-Liniger Bose gas, SciPost Phys. 3
2017
Later among the works it cites.
B. Doyon and H. Spohn, Dynamics of hard rods with initial domain wall state, J. Stat. Mech. 2017
2017
Later among the works it cites.
S. Friedli and Y. Velenik, Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction, Cambridge University Press, 2017
2017
Later among the works it cites.
E. Ilievski and J. De Nardis, Microscopic origin of ideal conductivity in integrable quantum models, Phys. Rev. Lett. 119
2017
Later among the works it cites.
E. Ilievski and J. De Nardis, Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach, Phys. Rev. B 96
2017
Later among the works it cites.
G. Misguich, K. Mallick, and P.L. Krapivsky, Dynamics of the spin-Heisenberg chain initialized in a domain-wall state, Phys. Rev. B 96
2017
Later among the works it cites.
L. Piroli, J. De Nardis, M. Collura, B. Bertini, and M. Fagotti, Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions, Phys. Rev. B 96
2017
Later among the works it cites.
H. Spohn, The Kardar-Parisi-Zhang equation - a statistical physics perspective, Les Houches Summer School July 2015 session CIV Stochastic processes and random matrices, edited by G. Schehr, A. Altland, Y.V. Fyodorov, N. O’Connell, and L.F. Cugliandolo. Oxford University Press, 2017
2017
Later among the works it cites.
A. Bastianello, B. Doyon, G. Watts, and T. Yoshimura, Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model, SciPost Phys. 4
2018
Later among the works it cites.
V. Bazhanov, P. Dorey, K. Kajiwara, and K. Takasaki, eds. Special issue on fifty years of the Toda lattice, J. Phys. A 51
2018
Later among the works it cites.
M. Collura, A. De Luca, and J. Viti, Analytic solution of the domain-wall nonequilibrium stationary state, Phys. Rev. B 97
2018
Later among the works it cites.
J. De Nardis, D. Bernard, and B. Doyon, Hydrodynamic diffusion in integrable systems, Phys. Rev. Lett. 121
2018
Later among the works it cites.
B. Doyon, Exact large-scale correlations in integrable systems out of equilibrium, SciPost Phys. 5
2018
Later among the works it cites.
B. Doyon, T. Yoshimura, and J.-S. Caux, Soliton gases and generalized hydrodynamics, Phys. Rev. Lett. 120
2018
Later among the works it cites.
T.K. Duy, On spectral measures of random Jacobi matrices, Osaka J. Math. 55
2018
Later among the works it cites.
F. Nakano and K.D. Trinh, Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics, J. Stat. Phys. 173
2018
Later among the works it cites.
V. Bulchandani, Xiangyu Cao, and J. Moore, Kinetic theory of quantum and classical Toda lattices, J. Phys. A 52
2019
Later among the works it cites.
V.B. Bulchandani and C. Karrasch, Subdiffusive front scaling in interacting integrable models, Phys. Rev. B 99
2019
Later among the works it cites.
Xiangyu Cao, V. Bulchandani, and H. Spohn, The GGE averaged currents of the classical Toda chain, J. Phys. A 52
2019
Later among the works it cites.
A. Das, M. Kulkarni, H. Spohn, and A. Dhar, Kardar-Parisi-Zhang scaling for an integrable lattice Landau-Lifshitz spin chain, Phys. Rev. E 100
2019
Later among the works it cites.
P. Deift, G. Dubach, and T. Trogdon, Universality in Numerical Computation, Courant Lecture Notes, Wiley, forthcoming. Based on lectures at the Courant Institute, 2019
2019
Later among the works it cites.
J. De Nardis, D. Bernard, and B. Doyon, Diffusion in generalized hydrodynamics and quasiparticle scattering, SciPost Phys. 6
2019
Later among the works it cites.
B. Doyon, Generalised hydrodynamics of the classical Toda system, J. Math. Phys. 60
2019
Later among the works it cites.
D. Karevski and G. Schütz, Charge-current correlation equalities for quantum systems far from equilibrium, SciPost Phys. 6
2019
Later among the works it cites.
M. Schemmer, I. Bouchoule, B. Doyon, and J. Dubail, Generalized hydrodynamics on an atom chip, Phys. Rev. Lett. 122
2019
Later among the works it cites.
N. Shiraishi, Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field, EPL 128
2019
Later among the works it cites.
D.-L. Vu and T. Yoshimura, Equations of state in generalized hydrodynamics, SciPost Phys. 6
2019
Later among the works it cites.
M. Borsi, B. Pozsgay, and L. Pristyák, Current operators in Bethe ansatz and generalized hydrodynamics: an exact quantum/classical correspondence, Phys. Rev. X 10
2020
Later among the works it cites.
2020
Later among the works it cites.
A. Das, K. Damle, A. Dhar, D. Huse, M. Kulkarni, C. Mendl, and H. Spohn, Nonlinear fluctuating hydrodynamics for the classical XXZ spin chain, J. Stat. Phys. 180
2020
Later among the works it cites.
B. Doyon, Lecture Notes on Generalised Hydrodynamics, SciPost Phys. Lecture Notes 18 (2020)
2020
Later among the works it cites.
A. Kuniba, G. Misguich and V. Pasquier, Generalized hydrodynamics in box-ball system, J. Phys. A: Math. Theor. 53
2020
Later among the works it cites.
A. Kuniba, G. Misguich and V. Pasquier, Generalized hydrodynamics in complete box-ball system for U q ( s l ^ n ) U_{q}(\hat{sl}^{n}) , arXiv
2020
Later among the works it cites.
2020
Later among the works it cites.
M. Mestyán and V. Alba, Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics, SciPost Phys. 8
2020
Later among the works it cites.
F. Moller and J. Schmiedmayer, Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models, SciPost Phys. 8
2020
Later among the works it cites.
Y. Nozawa and K. Fukai, Explicit construction of local conserved quantities in the XYZ spin- 1 2 \tfrac{1}{2} chain, Phys. Rev. Lett. 125
2020
Later among the works it cites.
B. Pozsgay, Current operators in integrable spin chains: lessons from long range deformations, SciPost Phys. 8
2020
Later among the works it cites.
H. Spohn, Generalized Gibbs ensembles of the classical Toda chain, J. Stat. Phys. 180
2020
Later among the works it cites.
H. Spohn, Ballistic space-time correlators of the classical Toda lattice, J. Phys. A 53
2020
Later among the works it cites.
H. Spohn, The collision rate ansatz for the classical Toda lattice, Phys Rev. E 101
2020
Later among the works it cites.
T. Yoshimura and H. Spohn, Collision rate ansatz for quantum integrable systems, SciPost Phys. 9
2020
Later among the works it cites.