Wave Turbulence and thermalization in one-dimensional chains

Onorato, M.; Lvov, Y.V.; Dematteis, G.; Chibbaro, S.

doi:10.1016/j.physrep.2023.09.006

Cited by 4 publications

(1 citation statement)

References 188 publications

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“…This á la Boltzmann approach involves equations for distributions derived under suitable assumptions. For instance, in the case of nonlinear lattices this leads to Boltzmann-Peierls [15] and wave turbulence equations [16] . For onedimensional chains this turned out to be useful to understand anomalous transport [17][18][19][20] and the effect of nonlinear resonances on (pre)thermalization [21,22].…”

Section: Introductionmentioning

confidence: 99%

Large-deviations approach to thermalization: the case of harmonic chains with conservative noise

Lepri

2024

J. Stat. Mech.

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We investigate the possibility of characterizing the different thermalization pathways through a large-deviation approach. Specifically, we consider clean, disordered and quasi-periodic harmonic chains under energy and momentum-conserving noise. For their associated master equations, describing the dynamics of normal modes energies, we compute the fluctuations of activity and dynamical entropy in the corresponding biased ensembles. First-order dynamical phase transition are found that originates from different activity regions in action space. At the transitions, the steady-state in the biased ensembles changes from extended to localized, yielding a kind of condensation in normal-modes space. For the disordered and quasi-periodic models, we argue that the phase-diagram has a critical point at a finite value of the disorder or potential strength.

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Section: Introductionmentioning

confidence: 99%

Large-deviations approach to thermalization: the case of harmonic chains with conservative noise

Lepri

2024

J. Stat. Mech.

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Recurrent nonlinear modulational instability in the β-FPUT chain

Armaroli,

Trillo

2024

Chaos, Solitons & Fractals

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Periodic orbits in Fermi–Pasta–Ulam–Tsingou systems

Karve,

Rose,

Campbell

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The Fermi–Pasta–Ulam–Tsingou (FPUT) paradox is the phenomenon whereby a one-dimensional chain of oscillators with nonlinear couplings shows long-lived nonergodic behavior prior to thermalization. The trajectory of the system in phase space, with a long-wavelength initial condition, closely follows that of the Toda model over short times, as both systems seem to relax quickly to a non-thermal, metastable state. Over longer times, resonances in the FPUT spectrum drive the system toward equilibrium, away from the Toda trajectory. Similar resonances are observed in q-breather spectra, suggesting that q-breathers are involved in the route toward thermalization. In this article, we first review previous important results related to the metastable state, solitons, and q-breathers. We then investigate orbit bifurcations of q-breathers and show that they occur due to resonances, where the q-breather frequencies become commensurate as mΩ1=Ωk. The resonances appear as peaks in the breather energy spectrum. Furthermore, they give rise to new “composite periodic orbits,” which are nonlinear combinations of multiple q-breathers that exist following orbit bifurcations. We find that such resonances are absent in integrable systems, as a consequence of the (extensive number of) conservation laws associated with integrability.

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Wave Turbulence and thermalization in one-dimensional chains

Cited by 4 publications

References 188 publications

Large-deviations approach to thermalization: the case of harmonic chains with conservative noise

Large-deviations approach to thermalization: the case of harmonic chains with conservative noise

Recurrent nonlinear modulational instability in the β-FPUT chain

Periodic orbits in Fermi–Pasta–Ulam–Tsingou systems

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