High-low pressure domain wall for the classical Toda lattice

Mendl, Christian B.; Spohn, Herbert

doi:10.21468/scipostphyscore.5.1.002

Cited by 5 publications

(4 citation statements)

References 29 publications

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“…( 23) with the input from the TBA equation for computing the effective velocity of the quasi-particle and analytically computed thermal expectation values. Exact numerical details of the relevant computation are given in [26], and a code is available at [37]. The circle and the stars are data from numerically solving the Euler-scale hydrodynamic equation at Gibbs equilibrium as in Eq.…”

Section: Resultsmentioning

confidence: 99%

“…For completeness, we first briefly review the basic concepts of the GHD in classical systems following the notation introduced in [16,26]. The DOS is represented as rρ p (r), where the distribution ρ p encodes all information of the conserved quantities.…”

Section: Generalized Hydrodynamics: Ghdmentioning

confidence: 99%

“…Earlier attempts at dynamic properties of the Toda chain are reviewed in [36]. After a gap in interest in Toda dynamics, recent development in the integrable hydrodynamic theory of Toda chain in [1,17], where the dynamics of single-point functions starting from domain wall initial conditions was addressed [26]. Accurate numerical results for the dynamics of twopoint functions were discussed in [21] and analytical results were only available in the limiting cases when the model was solvable.…”

Section: Toda Chainmentioning

confidence: 99%

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Integrable hydrodynamics of Toda chain: case of small systems

Kundu

2023

Eur. Phys. J. Spec. Top.

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Passing from a microscopic discrete lattice system with many degrees of freedom to a mesoscopic continuum system described by a few coarse-grained equations is challenging. The common folklore is to take the thermodynamic limit so that the physics of the discrete lattice describes the continuum results. The analytical procedure to do so relies on defining a small length scale (typically the lattice spacing) to coarse grain the microscopic evolution equations. Moving from the microscopic scale to the mesoscopic scale then requires careful approximations. In this work, we numerically test the coarsening in a Toda chain, which is an interacting integrable system, i.e., a system with a macroscopic number of conserved charges. Specifically, we study the spreading of fluctuations by computing the spatio-temporal thermal correlations with three different methods: (a) using microscopic molecular dynamics simulation with a large number of particles; (b) solving the generalized hydrodynamics equation; (c) solving the linear Euler scale equations for each conserved quantities. Surprisingly, the results for the small systems (c) match the thermodynamic results in (a) and (b) for macroscopic systems. This reiterates the importance and validity of integrable hydrodynamics in describing experiments in the laboratory, where we typically have microscopic systems.

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Section: Resultsmentioning

confidence: 99%

Section: Generalized Hydrodynamics: Ghdmentioning

confidence: 99%

Section: Toda Chainmentioning

confidence: 99%

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Integrable hydrodynamics of Toda chain: case of small systems

Kundu

2023

Eur. Phys. J. Spec. Top.

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“…To numerically solve the linearized GHD equations, we use a numerical method similar to the one from [33]. First, Eq.…”

Section: Details Of the Numerical Implementation 411 Solving Lineariz...mentioning

confidence: 99%

Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

Mazzuca¹,

Грава²,

Kriecherbauer³

et al. 2023

Preprint

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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 compared 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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Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

Mazzuca,

Grava,

Kriecherbauer

et al. 2023

J Stat Phys

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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 compared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is $$N=3000,4000$$ N = 3000 , 4000 and time $$t =600$$ 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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High-low pressure domain wall for the classical Toda lattice

Cited by 5 publications

References 29 publications

Integrable hydrodynamics of Toda chain: case of small systems

Integrable hydrodynamics of Toda chain: case of small systems

Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

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