Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

Guido  Mazzuca; Tamara Grava; Thomas Kriecherbauer; Kenneth T.-R. McLaughlin; Christian B. Mendl; Herbert  Spohn

doi:10.1007/s10955-023-03155-x

Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

Guido Mazzuca^*, Tamara Grava, Thomas Kriecherbauer, Kenneth T.-R. McLaughlin, Christian B. Mendl, Herbert Spohn

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

Abstract

We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and energy are computed numerically over a wide range of pressure and temperature. Our numerical results are com- pared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is N = 3000, 4000 and time t = 600, at which ballistic scaling is well confirmed. With no adjustable parameters, the numerically obtained scaling functions agree with the theory within a precision of less than 3.5%.

Original language	English
Article number	149
Number of pages	22
Journal	Journal of Statistical Physics
Volume	190
Issue number	8
DOIs	https://doi.org/10.1007/s10955-023-03155-x
Publication status	Published - 25 Aug 2023

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. 1440140, while five of the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the fall semester of 2021. We thank both reviewers for illuminating comments and suggestions. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves" where some work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. TG acknowledges the support of the European Union’s H2020 Marie Skłodowska–Curie grant No. 778010 IPaDEGAN, of INdAM/GNFM and of the research project Mathematical Methods in NonLinear Physics (MMNLP), Gruppo 4-Fisica Teorica of INFN. GM is financed by the KAM grant number 2018.0344. KTRM was supported by a Visiting Wolfson research fellowship from the Royal Society.

Publisher Copyright:
© 2023, The Author(s).

Keywords

correlation functions
Toda lattice
generalized Hydrodynamic

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title = "Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale",

abstract = "We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and energy are computed numerically over a wide range of pressure and temperature. Our numerical results are com- pared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is N = 3000, 4000 and time t = 600, at which ballistic scaling is well confirmed. With no adjustable parameters, the numerically obtained scaling functions agree with the theory within a precision of less than 3.5%.",

keywords = "correlation functions, Toda lattice, generalized Hydrodynamic",

author = "Guido Mazzuca and Tamara Grava and Thomas Kriecherbauer and McLaughlin, {Kenneth T.-R.} and Mendl, {Christian B.} and Herbert Spohn",

note = "Funding Information: This material is based upon work supported by the National Science Foundation under Grant No. 1440140, while five of the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the fall semester of 2021. We thank both reviewers for illuminating comments and suggestions. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves{"} where some work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. TG acknowledges the support of the European Union{\textquoteright}s H2020 Marie Sk{\l}odowska–Curie grant No. 778010 IPaDEGAN, of INdAM/GNFM and of the research project Mathematical Methods in NonLinear Physics (MMNLP), Gruppo 4-Fisica Teorica of INFN. GM is financed by the KAM grant number 2018.0344. KTRM was supported by a Visiting Wolfson research fellowship from the Royal Society. Publisher Copyright: {\textcopyright} 2023, The Author(s).",

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N1 - Funding Information: This material is based upon work supported by the National Science Foundation under Grant No. 1440140, while five of the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the fall semester of 2021. We thank both reviewers for illuminating comments and suggestions. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves" where some work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. TG acknowledges the support of the European Union’s H2020 Marie Skłodowska–Curie grant No. 778010 IPaDEGAN, of INdAM/GNFM and of the research project Mathematical Methods in NonLinear Physics (MMNLP), Gruppo 4-Fisica Teorica of INFN. GM is financed by the KAM grant number 2018.0344. KTRM was supported by a Visiting Wolfson research fellowship from the Royal Society. Publisher Copyright: © 2023, The Author(s).

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N2 - We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and energy are computed numerically over a wide range of pressure and temperature. Our numerical results are com- pared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is N = 3000, 4000 and time t = 600, at which ballistic scaling is well confirmed. With no adjustable parameters, the numerically obtained scaling functions agree with the theory within a precision of less than 3.5%.

AB - We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and energy are computed numerically over a wide range of pressure and temperature. Our numerical results are com- pared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is N = 3000, 4000 and time t = 600, at which ballistic scaling is well confirmed. With no adjustable parameters, the numerically obtained scaling functions agree with the theory within a precision of less than 3.5%.

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KW - generalized Hydrodynamic

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M1 - 149

ER -

Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

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