Antipersistent energy-current correlations in strong long-ranged Fermi-Pasta-Ulam-Tsingou-type models

We study heat transfer in one-dimensional Fermi-Pasta-Ulam-Tsingou-type systems with long-range (LR) interactions. The strength of the LR interaction between two lattice sites decays as a power $\sigma$ of the inverse of their distance. We focus on the strong LR regime ($0\le \sigma \le 1$) and show that the thermal transport behaviors are remarkably nuanced. Specifically, we observe that the antipersistent (negative) energy current correlation in this regime is intricately dependent on $\sigma$, displaying a nonmonotonic variation. Notably, a significant qualitative change occurs at ${\sigma }_c=0.5$, where with respect to other $\sigma$ values the correlation shows a minimum negative value. Furthermore, our findings also demonstrate that within the long-time range considered, these antipersistent correlations will eventually vanish for certain $\sigma >0.5$. The underlying mechanisms behind these intriguing phenomena are related to the crossover of two diverse space-time scaling properties of equilibrium heat correlations and the various scattering processes of phonons and discrete breathers.

Figure 1

Equilibrium heat current autocorrelation $C_{JJ}\left(t\right)$ vs $t$ for several $\sigma$ within the LR strong regime (with $0\le \sigma \le 1$). For a better visualization, the correlation values have been rescaled between 0 and 1 by dividing them by $C_{JJ}\left(0\right)$.

Figure 2

Equilibrium spatiotemproal correlation function of heat ${\rho }_Q(m,t)$ for several $0\le \sigma \le 1$ for three typical long times: $t=1000$ (dotted), $t=2000$ (dashed), and $t=4000$ (solid).

Figure 3

(a) A single log plot of ${\rho }_Q(0,t)$ vs $t$ for describing an exponential decay for $\sigma =0$, 0.25, 0.4 and 0.5; (b) A log-log plot of ${\rho }_Q(0,t)$ vs $t$ for describing a power-law decay for $\sigma =0.5$, 0.6, 0.8, and 1. The two dashed lines are a guide for the two distinct laws.

Figure 4

${\rho }_Q(0,t)$ vs $t$ in a single-log plot showing the detailed two-stage exponential decay for (a) $\sigma =0$, (b) $\sigma =0.25$, (c) $\sigma =0.4$, and (d) $\sigma =0.5$.

Figure 5

${\rho }_Q(0,t)$ vs $t$ in a single-log plot showing the detailed variation around $\sigma =0.5$.

Figure 6

${\rho }_Q(0,t)$ vs $t$ in a log-log plot showing the detailed power-law decay in long times for (a) $\sigma =0.6$, (b) $\sigma =0.7$, (c) $\sigma =0.8$, and (d) $\sigma =1$.

Figure 7

Snapshots of particle's momentum $p_i$ vs $i$ at a given long time $t=7000$, after initially applying two kicks at $i=1$ and $i=2205$ with momenta $p_1=-0.7$ and $p_{2205}=0.7$ (corresponding to a averaged temperature of $T=0.5$), respectively. The insets in (a)–(e) are a zoom for the typical moving excitations for the given $\sigma$.