Normal heat conduction in one-dimensional momentum conserving lattices with asymmetric interactions

Zhong, Yi; Zhang, Yong; Wang, Jiao; Zhao, Hong

doi:10.1103/physreve.85.060102

Cited by 85 publications

(93 citation statements)

References 35 publications

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“…Such a situation has been observed for the FPU-α + β model and for chains of oscillators coupled through a Lennard-Jones potential [31]. The authors provided an explanation of their results by arguing that the scattering of long-wavelength phonons could be attributed to the spontaneous formation of macroscopic mass gradients along the chain, typical of asymmetric interaction potentials acting between nonlinear oscillators [32]. The same authors also speculated that the exponent γ = 1/3 is observed in the HPG, because in a gaslike model the asymmetry of the interaction is much less effective in producing macroscopic density fluctuations.…”

Section: Introductionmentioning

confidence: 82%

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

et al. 2015

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We study the anomalous dynamical scaling of equilibrium correlations in one-dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through multiparticle collision dynamics. For both models-that admit three conservation laws-by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.

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Section: Introductionmentioning

confidence: 82%

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

et al. 2015

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“…The inherent asymmetry of the interaction potential yields a nonvanishing internal pressure [43,44]. Figure 5 depicts the response function for the FPU-αβ lattice.…”

Section: B Fpu-αβ Latticementioning

confidence: 99%

Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean-free paths

Liu

Hänggi

et al. 2014

Phys. Rev. B

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Guided by a stylized experiment we develop a self-consistent anharmonic phonon concept for nonlinear lattices which allows for explicit "visualization." The idea uses a small external driving force which excites the front particles in a nonlinear lattice slab and subsequently one monitors the excited wave evolution using molecular dynamics simulations. This allows for a simultaneous, direct determination of the existence of the phonon mean-free path with its corresponding anharmonic phonon wave number as a function of temperature. The concept for the mean-free path is very distinct from known prior approaches: the latter evaluate the mean-free path only indirectly, via using both a scale for for the phonon relaxation time and yet another one for the phonon velocity. Notably, the concept here is neither limited to small lattice nonlinearities nor to small frequencies. The scheme is tested for three strongly nonlinear lattices of timely current interest which either exhibit normal or anomalous heat transport.

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“…Coming back to 1D model chains, up to now, many ingredients related to anomalous thermal conduction have been carefully considered, among them are chaos [28][29][30][31][32][33], conservation of momentum [34][35][36][37], asymmetric interactions [38][39][40][41][42], linearity [33,[43][44][45][46], integrability [47], pressure [48,49], surface scattering effect [50] etc. Particularly, the viewpoint that a system with (without) a momentum conservation property should disobey (obey) Fourier's law has been widely accepted, although there are still some contradictory results on this issue [51][52][53][54][55][56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

2017

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Anomalous (non-Fourier's) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier's) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentumnonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving φ 4 model and present evidence that the mobile discrete breathers or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band can be responsible for that.

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Normal heat conduction in one-dimensional momentum conserving lattices with asymmetric interactions

Cited by 85 publications

References 35 publications

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean-free paths

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

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