Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction

We numerically investigate the heat transport problem in a one-dimensional momentum-conserving lattice with a soft-type (ST) anharmonic interparticle interaction. It is found that with the increase of the system's temperature, while the introduction of ST anharmonicity softens phonons and decreases their velocities, this type of nonlinearity like its hard type (HT) counterpart, can still not be able to fully damp the longest wavelength phonons. Therefore, a usual anomalous temperature dependence of heat transport with certain scaling properties similarly to those shown in the Fermi-Pasta-Ulam-$\beta$-like systems with HT interactions can be seen. Our detailed examination from simulations verifies this temperature-dependent behavior well.

Figure 1

The ST anharmonic interparticle potential [Eq. (2), solid] (a) and its associated force (b). For comparison we also plot the cases of the harmonic (dashed) and FPU-$\beta$ (dotted) systems.

Figure 2

Profiles of ${\rho }_Q(m,t)$ for three long times $t=200$ (dotted), $t=400$ (dashed), and $t=600$ (solid) under temperatures $T=0.001$ (a), $T=0.0075$ (b), $T=0.075$ (c), and $T=0.75$ (d), respectively.

Figure 3

Rescaled ${\rho }_Q(m,t)$, the focused temperatures here are the same as those in Fig. 2.

Figure 4

Exponents $q\nu \left(q\right)$ vs $q$ for indicating the bilinear scaling behavior. Here we take the case of $T=0.75$ as an example.

Figure 5

$\gamma$ vs $T$; the horizontal dashed lines, from bottom to top, denote $\gamma =1$, $\gamma =3/2$, and $\gamma =5/3$, respectively.

Figure 6

Momentum spread ${\rho }_p(m,t)$ for three long time $t=200$ (dotted), $t=400$ (dashed), and $t=600$ (solid) under temperatures $T=0.001$ (a), $T=0.0075$ (b), $T=0.075$ (c), and $T=0.75$ (d), respectively.

Figure 7

The sound velocity $c$ vs $T$, where the dashed line denotes the predictions of formula (6).

Figure 8

Phonon spectrum $P\left(\omega \right)$ for different temperatures: (a) $T=0.001$, (b) $T=0.0075$, (c) $T=0.075$, (d) $T=0.75$, respectively.

Figure 9

A log-log plot of Fig. 8, where the dotted lines denote the frequencies ${\omega }_{\mathrm{D}}$ below which phonons are damped very weakly.

Figure 10

The averaged frequency $\overline{\omega }$ of phonons shown in $P\left(\omega \right)$ vs $T$.