Nearly separable behavior of Fermi-Pasta-Ulam chains through the stochasticity threshold

Alabiso, Carlo; Casartelli, Mario; Marenzoni, Paolo

doi:10.1007/bf02179398

Cited by 47 publications

(65 citation statements)

References 4 publications

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“…The existing quasi-harmonic theories of this model all focus on this particular case [4,5,[7][8][9][10][11]. In this part, we not only present the comparison between our approach and MD results, but also point out the connections between our approach and some of the existing quasi-harmonic theories.…”

Section: A P =mentioning

confidence: 91%

“…Hence we should look for inequalities for the Gibbs free energy G. To do this, we introduce a reference system with a Hamiltonian H 0 and prepare the original system and the reference system at same pressure. Then following this spirit, we integrate both sides of the following equality ρ(q, p) = ρ 0 (q, p)e −βT (H−H0)−βT (G0−G) (4) over the whole phase space to yield…”

Section: A the Variational Principlesmentioning

confidence: 99%

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Renormalized phonons in nonlinear lattices: A variational approach

Liu

et al. 2015

Phys. Rev. E

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We propose a variational approach to study renormalized phonons in momentum conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure to phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one dimensional nonlinear lattices with a symmetric or asymmetric Fermi-PastaUlam type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which beyond the scope of existing theories, including those having the symmetric potential and pressure, and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.

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Section: A P =mentioning

confidence: 91%

Section: A the Variational Principlesmentioning

confidence: 99%

Renormalized phonons in nonlinear lattices: A variational approach

Liu

et al. 2015

Phys. Rev. E

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“…The existence of renormalized phonons has been independently discovered by many research groups during the study of lattice vibrations [1,2], field thermalization [3], and nonlinear waves [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…For nonlinear lattices, the collective motion under the effect of nonlinear interactions gives rise to the surprisingly weak interactions among the so-called renormalized phonons [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Scaling of temperature-dependent thermal conductivities for one-dimensional nonlinear lattices

2013

Phys. Rev. E

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In general nonlinear lattices, the existence of renormalized phonons due to the nonlinear interactions has been independently discovered by many research groups. Regarding these renormalized phonons as the energy carriers responsible for the heat transport, the scaling laws of temperature-dependent thermal conductivities of one-dimensional nonlinear lattices can be derived from the phenomenological effective phonon approach. For the paradigmatic nonlinear φ(4) lattice, κ(T)[proportionality]T(-1.35), which was numerically obtained more than a decade ago, can be well explained by the current approach. Most importantly, this approach is able to predict the scaling laws of temperature-dependent thermal conductivities of generalized nonlinear Klein-Gordon lattices. These theoretical predictions are compared by numerical simulations, and perfect agreements have been found.

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“…One method of addressing the issue is the so-termed renormalized phonon picture [10][11][12][13][14][15]. In essence, this approach uses an effective harmonic approximation of the nonlinear interaction forces via a temperature-renormalized phonon dispersion.…”

Section: Introductionmentioning

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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Nearly separable behavior of Fermi-Pasta-Ulam chains through the stochasticity threshold

Cited by 47 publications

References 4 publications

Renormalized phonons in nonlinear lattices: A variational approach

Renormalized phonons in nonlinear lattices: A variational approach

Scaling of temperature-dependent thermal conductivities for one-dimensional nonlinear lattices

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

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