Ballistic transport in the classical Toda chain with harmonic pinning

Lebowitz, Joel L.; Scaramazza, Jasen A.

doi:10.48550/arxiv.1801.07153

Cited by 7 publications

(13 citation statements)

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“…It has been observed in a few recent studies that depending on the form of the integrability-breaking term and other parameters such as temperature, the crossover can occur at extremely large system sizes. Following some preliminary results by two of the present authors [30], this was further investigated in [31] which demonstrated that the crossover to diffusive transport in the quadratically pinned Toda chain occurs at very large length scales. This was then attributed to the fact that solitons are the main energy carriers in this system and the quadratic pinning potential affects them rather weakly.…”

Section: Introductionmentioning

confidence: 80%

Transport Properties of the Classical Toda Chain: Effect of a Pinning Potential

et al. 2019

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We consider energy transport in the classical Toda chain in the presence of an additional pinning potential. The pinning potential is expected to destroy the integrability of the system and an interesting question is to see the signatures of this breaking of integrability on energy transport. We investigate this by a study of the non-equilibrium steady state of the system connected to heat baths as well as the study of equilibrium correlations. Typical signatures of integrable systems are a size-independent energy current, a flat bulk temperature profile and ballistic scaling of equilibrium dynamical correlations, these results being valid in the thermodynamic limit. We find that, as expected, these properties change drastically on introducing the pinning potential in the Toda model. In particular, we find that the effect of a harmonic pinning potential is drastically smaller at low temperatures, compared to a quartic pinning potential. We explain this by noting that at low temperatures the Toda potential can be approximated by a harmonic inter-particle potential for which the addition of harmonic pinning does not destroy integrability.

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Section: Introductionmentioning

confidence: 80%

Transport Properties of the Classical Toda Chain: Effect of a Pinning Potential

et al. 2019

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“…In this paper we focus on the study of a one-dimensional Toda lattice of N particles in the presence of a pinning potential, whose Hamiltonian reads [33]…”

Section: The Pinned Toda Chainmentioning

confidence: 99%

“…The present work is organized as follows. In Section 2 we present the main model, the pinned Toda chain first considered in this context in [33] and discuss qualitatively its dynamics. In Section 3, we compute the Lyapunov exponents of the model to show that the pinning generically destroys integrability.…”

Section: Introductionmentioning

confidence: 99%

Transport in perturbed classical integrable systems: The pinned Toda chain

Cintio

Iubini

Lepri

et al. 2018

Chaos, Solitons & Fractals

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Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [arXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by computing the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.

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“…Refs. [25][26][27][28] for some recent related results). Precisely because of mathematical and conceptual simplicity of the model we hope that further analytic progress will be possible in future.…”

Section: Discussionmentioning

confidence: 89%

On two reversible cellular automata with two particle species

Klobas,

Prosen

2021

Preprint

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We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible cellular automaton when only a single species of particles is present, and satisfy the requirements of flavour exchange (C), space-reversal (P ), and time-reversal (T ) symmetries. We find closed-form expressions for three local conserved charges and provide an explicit matrix product form of the grand canonical Gibbs states, which are identical for both models. For one of the models this family of Gibbs states seems to be a complete characterisation of equilibrium (i.e. space and time translation invariant) states, while for the other model we empirically find a sequence of local conserved charges, one for each support size larger than 2, hinting to its algebraic integrability. Finally, we numerically investigate the behaviour of spatio-temporal correlation functions of charge densities, and test the prediction of nonlinear fluctuating hydrodynamics for the model with exactly three local charges. The numerically observed 'sound velocity' deviates from the hydrodynamic prediction. The deviations are either significant, or they decay extremely slowly with the simulation time, which leaves us with an open question for the mechanism of such a glassy behaviour in a deterministic locally interacting system.

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Ballistic transport in the classical Toda chain with harmonic pinning

Cited by 7 publications

References 0 publications

Transport Properties of the Classical Toda Chain: Effect of a Pinning Potential

Transport Properties of the Classical Toda Chain: Effect of a Pinning Potential

Transport in perturbed classical integrable systems: The pinned Toda chain

On two reversible cellular automata with two particle species

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