Effective phonons in anharmonic lattices: Anomalous
                    <i>vs.</i>
                    normal heat conduction

Li, Nianbei; Tong, Peiqing; Li, Baowen

doi:10.1209/epl/i2006-10079-7

Cited by 64 publications

(85 citation statements)

References 15 publications

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“…The corresponding sound velocity √ K L is exactly the same as that predicted by the effective phonon theory (EPT) [8,12] based on the generalized equipartition theorem [33] as well as the nonlinear fluctuating hydrodynamics (NFH) using the hydrodynamic approximation [29,34,35], although the NFH is not an effective theory for phonons.…”

Section: A P =supporting

confidence: 54%

“…A renormalized phonon (r-ph) picture was then put forward independently by several groups using varying techniques [4][5][6][7][8][9][10][11]. Within the scope of this picture, one can successfully interpret and understand a wide range of physical phenomena, including a theoretical description of the sound velocity [12] as well as scaling laws of thermal conductivity κ(T ) with temperature T [10,13].…”

Section: Introductionmentioning

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 =supporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Renormalized phonons in nonlinear lattices: A variational approach

Liu

et al. 2015

Phys. Rev. E

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“…[62]. This power-law dependence of κ(T ) ∝ T −3.2 cannot be explained by the effective phonon theory which is able to predict the temperature dependent thermal conductivities for other typical 1D nonlinear lattices such as FPU-β lattice and generalized nonlinear Klein-Gordon lattices [68][69][70][71][72][73][74][75]. According to the effective phonon theory, the thermal conductivity for low temperature rotator lattice with Hamiltonian of Eq.…”

Section: Resultsmentioning

confidence: 99%

Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

2015

Eur. Phys. J. B

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In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam β (FPU-β) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.

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“…[25]), the quantity M(ω) is an integer equal to the number of propagating modes. In the anharmonic FPU chain, however, the anharmonicity both renormalizes the phonon modes [30] and generates a finite phonon life-time, shifting the dispersion to higher frequencies and dissipating phonons also in the leads. Therefore M(ω) now cannot be interpreted simply as the number of modes and instead it should be taken as the spectral current for N → 0 + .…”

Section: B Mean Free Pathsmentioning

confidence: 99%

Nonequilibrium phonon mean free paths in anharmonic chains

et al. 2015

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Harnessing the power of low-dimensional materials in thermal applications calls for a solid understanding of the anomalous thermal properties of such systems. We analyze thermal conduction in one-dimensional systems by determining the frequency-dependent phonon mean free paths (MFPs) for an anharmonic chain, delivering insight into the diverging thermal conductivity observed in computer simulations. In our approach, the MFPs are extracted from the length dependence of the spectral heat current obtained from nonequilibrium molecular dynamics simulations. At low frequencies, the results reveal a power-law dependence of the MFPs on frequency, in agreement with the diverging conductivity and the recently determined equilibrium MFPs. At higher frequencies, however, the nonequilibrium MFPs consistently exceed the equilibrium MFPs, highlighting the differences between the two quantities. Exerting pressure on the chain is shown to suppress the mean free paths and to generate a weaker divergence of MFPs at low frequencies. The results deliver important insight into the anomalous thermal conduction in low-dimensional systems and also reveal differences between the MFPs obtained from equilibrium and nonequilibrium simulations.

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Effective phonons in anharmonic lattices: Anomalous vs. normal heat conduction

Cited by 64 publications

References 15 publications

Renormalized phonons in nonlinear lattices: A variational approach

Renormalized phonons in nonlinear lattices: A variational approach

Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

Nonequilibrium phonon mean free paths in anharmonic chains

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