Bulk properties of anharmonic chains in strong thermal gradients: non-equilibrium φ4 theory

Aoki, Kenichiro; Kusnezov, Dimitri

doi:10.1016/s0375-9601(99)00899-3

Cited by 129 publications

(130 citation statements)

References 33 publications

(33 reference statements)

Supporting

Mentioning

116

Contrasting

Order By: Relevance

“…We increase N and examine if the bulk limit is reached to finally extract κ for given T, δ. Bulk behavior had already been observed when δ = 1/2 [20,21], and we do so also in the present study.…”

Section: Thermal Conductivity From Molecular Dynamicssupporting

confidence: 90%

“…We use free boundary conditions, which means q j+1 = q j at the boundaries, but the physical results are insensitive to this particular choice of boundary conditions. We adopt deterministic thermostats which generalize those of Nosé-Hoover [18,19], and follow the methods used for the chain when δ = 1/2 [16,20]. The non-equilibrium steady state is achieved by integrating the equations of motion and physical observables are measured by averaging over time after waiting for a sufficiently long equilibration time span.…”

Section: Thermal Conductivity From Molecular Dynamicsmentioning

confidence: 99%

“…Comparing to the case f + (0) = 1 and f − (ℓ) = 1, one concludes that the imposed right boundary temperature is T + = 2 and correspondingly the imposed left boundary temperature T − = 0. The solution to (6.17), (6.18) reads 19) which yields the temperature profile 20) and the steady state current J(ℓ) for slab length ℓ as…”

Section: Steady State Temperature Profilementioning

confidence: 99%

See 2 more Smart Citations

Energy Transport in Weakly Anharmonic Chains

2006

Self Cite

View full text Add to dashboard Cite

Abstract.We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.

show abstract

Section: Thermal Conductivity From Molecular Dynamicssupporting

confidence: 90%

Section: Thermal Conductivity From Molecular Dynamicsmentioning

confidence: 99%

Section: Steady State Temperature Profilementioning

confidence: 99%

See 1 more Smart Citation

Energy Transport in Weakly Anharmonic Chains

2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…Using traditional arguments, we would take a larger box containing x ′ and assume that on the larger scale, the behavior is closer to local equilibrium. In examining (9) we see that it is a positive definite function of position (up to the overall sign of C A ). So any averaging over a larger box will not necessarily converge to δA/A = 0, required for local equilibrium.…”

Section: Some Results From Classical Non-equilibrium Statistical mentioning

confidence: 90%

Non-equilibrium Statistical Mechanics of Classical and Quantum Systems

Kusnezov

Lutz

Aoki

2002

Dynamics of Dissipation

View full text Add to dashboard Cite

show abstract

“…Evidence of a finite conductivity for the case a = 0 has been reported in [167,168]. Two further examples were analyzed, the sine-Gordon and bounded single-well potentials:…”

Section: Force Laws That Predict Classical Heat Conductivity:coupled-mentioning

confidence: 98%

Dynamics of Oscillator Chains

Lichtenberg

Livi

Pettini

et al.

The Fermi-Pasta-Ulam Problem

View full text Add to dashboard Cite

Abstract. The Fermi-Pasta-Ulam (FPU) nonlinear oscillator chain has proved to be a seminal system for investigating problems in nonlinear dynamics. First proposed as a nonlinear system to elucidate the foundations of statistical mechanics, the initial lack of confirmation of the researchers expectations eventually led to a number of profound insights into the behavior of high-dimensional nonlinear systems. The initial numerical studies, proposed to demonstrate that energy placed in a single mode of the linearized chain would approach equipartition through nonlinear interactions, surprisingly showed recurrences. Although subsequent work showed that the origin of the recurrences is nonlinear resonance, the question of lack of equipartition remained. The attempt to understand the regularity bore fruit in a profound development in nonlinear dynamics: the birth of soliton theory. A parallel development, related to numerical observations that, at higher energies, equipartition among modes could be approached, was the understanding that the transition with increasing energy is due to resonance overlap. Further numerical investigations showed that time-scales were also important, with a transition between faster and slower evolution. This was explained in terms of mode overlap at higher energy and resonance overlap at lower energy. Numerical limitations to observing a very slow approach to equipartition and the problem of connecting high-dimensional Hamiltonian systems to lower dimensional studies of Arnold diffusion, which indicate transitions from exponentially slow diffusion along resonances to power-law diffusion across resonances, have been considered. Most of the work, both numerical and theoretical, started from low frequency (long wavelength) initial conditions. Coincident with developments to understand equipartition was another program to connect a statistical phenomenon to nonlinear dynamics, that of understanding classical heat conduction. The numerical studies were quite different, involving the excitation of a boundary oscillator with chaotic motion, rather than the excitation of

show abstract

Bulk properties of anharmonic chains in strong thermal gradients: non-equilibrium φ4 theory

Cited by 129 publications

References 33 publications

Energy Transport in Weakly Anharmonic Chains

Energy Transport in Weakly Anharmonic Chains

Non-equilibrium Statistical Mechanics of Classical and Quantum Systems

Dynamics of Oscillator Chains

Contact Info

Product

Resources

About