Analytical measure of temperature for nonlinear dynamical systems

Liu, Yue; He, Dahai

doi:10.1103/physreve.100.052143

Phys. Rev. E

2019

DOI: 10.1103/physreve.100.052143

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Analytical measure of temperature for nonlinear dynamical systems

Yue Liu

Dahai He

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2021

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Cited by 2 publications

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“…[28−30] In literature, SCPT, which can be traced back to Feynman, [14] has been developed to study the properties of thermal conduction in low-dimensional nonlinear lattices [15−19] and the temperature of microcanonical ensemble. [33] Without loss of generality, we consider the Hamiltonian of a one-dimensional homogeneous system in the form of…”

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Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear Lattices

Liu¹,

He²

2021

Chinese Phys. Lett.

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Based on the self-consistent phonon theory, the spectral energy density is calculated by the canonical transformation and the Fourier transformation. Through fitting the spectral energy density by the Lorentzian profile, the phonon frequency as well as the phonon relaxation time is obtained in one-dimensional nonlinear lattices, which is validated in the Fermi–Pasta–Ulam-β (FPU-β) and ϕ 4 lattices at different temperatures. The phonon mean free path is then evaluated in terms of the phonon relaxation time and phonon group velocity. The results show that, in the FPU-β lattice, the phonon mean free path as well as the phonon relaxation time displays divergent power-law behavior. The divergent exponent coincides well with that derived from the Peierls–Boltzmann theory at weak anharmonic nonlinearity. The value of the divergent exponent expects a power-law divergent heat conductivity with system size, which violates Fourier’s law. For the ϕ 4 lattice, both the phonon relaxation time and mean free path are finite, which ensures normal heat conduction.

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Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear Lattices

Liu¹,

He²

2021

Chinese Phys. Lett.

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Analytical approach to Lyapunov time: Universal scaling and thermalization

Liu

2021

Phys. Rev. E

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Analytical measure of temperature for nonlinear dynamical systems

Cited by 2 publications

References 32 publications

Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear Lattices

Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear Lattices

Analytical approach to Lyapunov time: Universal scaling and thermalization

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