Coexistence of Ballistic and Fourier Regimes in the 
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 Fermi-Pasta-Ulam-Tsingou Lattice

Dematteis, Giovanni; Rondoni, Lamberto; Proment, Davide; Vita, Francesco De; Onorato, Miguel

doi:10.1103/physrevlett.125.024101

Cited by 19 publications

(13 citation statements)

References 42 publications

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“…Further analysis in [19] gives a derivation of the ballistic scaling for the Toda lattice. The decay of equilibrium correlation functions show 1 similar features as anomalous heat transport in one-dimensional systems [2,3,7] which leads to conjecture that the two phenomena are related [8].…”

Section: Introductionmentioning

confidence: 89%

“…The quantities 1 ( j, t) and 2 ( j, t) can be expressed as sums of independent centered Gaussian random variables and are therefore also Gaussian random variables with zero mean and variance ( 1 ( j, t)) 2 and ( 2 ( j, t)) 2 , where all the averages are taken with respect to the distribution (1.9), see also (2.10). We calculate the variance for the case of the harmonic oscillator with nearest neighbour interactions.…”

Section: Currents and Potentialsmentioning

confidence: 99%

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Correlation Functions for a Chain of Short Range Oscillators

et al. 2021

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We consider a system of harmonic oscillators with short range interactions and we study their correlation functions when the initial data is sampled with respect to the Gibbs measure. Such correlation functions display rapid oscillations that travel through the chain. We show that the correlation functions always have two fastest peaks which move in opposite directions and decay at rate $$t^{-\frac{1}{3}}$$ t - 1 3 for position and momentum correlations and as $$t^{-\frac{2}{3}}$$ t - 2 3 for energy correlations. The shape of these peaks is asymptotically described by the Airy function. Furthermore, the correlation functions have some non generic peaks with lower decay rates. In particular, there are peaks which decay at rate $$t^{-\frac{1}{4}}$$ t - 1 4 for position and momentum correlators and with rate $$t^{-\frac{1}{2}}$$ t - 1 2 for energy correlators. The shape of these peaks is described by the Pearcey integral. Crucial for our analysis is an appropriate generalisation of spacings, i.e. differences of the positions of neighbouring particles, that are used as spatial variables in the case of nearest neighbour interactions. Using the theory of circulant matrices we are able to introduce a quantity that retains both localisation and analytic viability. This also allows us to define and analyse some additional quantities used for nearest neighbour chains. Finally, we study numerically the evolution of the correlation functions after adding nonlinear perturbations to our model. Within the time range of our numerical simulations the asymptotic description of the linear case seems to persist for small nonlinear perturbations while stronger nonlinearities change shape and decay rates of the peaks significantly.

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Section: Introductionmentioning

confidence: 89%

Section: Currents and Potentialsmentioning

confidence: 99%

Correlation Functions for a Chain of Short Range Oscillators

et al. 2021

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“…This shows that the heat transport mechanism of the UFL is quite different from that of the FPU lattice, which exhibits the non-ballistic anomalous heat transport. In the FPU lattice, only the normal modes with small k make a dominant contribution while J H is strongly suppressed for the other larger k as N increases [20]. This suggests that those small k modes form solitons and they induce the anomalous heat transport in the FPU lattice.…”

Section: Non-conserving Conservingmentioning

confidence: 97%

“…Ding-a-ling [10,11] Ding-dong [12] Frenkel-Kontrova [13] φ 4 chain [14,15] Toda+harmonic on-site [16] Coupled rotators [17] Anomalous 0 < α < 1 FPU-α [18] FPU-β [19,20] Diatomic Toda [21] Ballistic α = 1 UFL Toda [22] TABLE I: Classification of lattice models by the type of heat transport and the total momentum conservation property.…”

Section: Non-conserving Conservingmentioning

confidence: 99%

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Heat transport in nonlinear lattices free from the Umklapp process

Yoshimura,

Doi,

Kitamura

2021

Preprint

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We construct one-dimensional nonlinear lattices having the special property such that the Umklapp process vanishes and only the normal processes are included in the potential functions. We study heat transport in these lattices by non-equilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs, i.e., the scaling law κ ∝ N holds between the thermal conductivity κ and the lattice size N. This result directly validates Peierls's hypothesis that only the Umklapp processes can cause the thermal resistance while the normal one do not.

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Anomalous heat transport and universality in macroscopic diffusion models

Bernardi,

Pizzi,

Rondoni

2024

J Therm Anal Calorim

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Anomalous diffusion is ubiquitous in nature and relevant for a wide range of applications, including energy transport, especially in bio- and nano-technologies. Numerous approaches have been developed to describe it from a microscopic point of view, and recently, it has been framed within universality classes, characterized by the behaviour of the moments and auto-correlation functions of the transported quantities. It is important to investigate whether such universality applies to macroscopic models. Here, the spectrum of the moments of the solutions of the transport equations is investigated for three continuous PDE models featuring anomalous diffusion. In particular, we consider the transport described by: (i) a generalized diffusion equation with time-dependent diffusion coefficient; (ii) the Porous Medium Equation and (iii) the Telegrapher Equation. For each model, the key features of the source-type solution as well as the analytical results for the moment analysis are revisited and extended via both analytical and numerical approaches. Equivalence of the asymptotic behaviour of the corresponding heat transport is confirmed within the realm of weak anomalous diffusion.

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Coexistence of Ballistic and Fourier Regimes in the β Fermi-Pasta-Ulam-Tsingou Lattice

Cited by 19 publications

References 42 publications

Correlation Functions for a Chain of Short Range Oscillators

Correlation Functions for a Chain of Short Range Oscillators

Heat transport in nonlinear lattices free from the Umklapp process

Anomalous heat transport and universality in macroscopic diffusion models

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