Predicting and identifying finite-size effects in current spectra of one-dimensional oscillator chains

The existence of a finite-size effect in one-dimensional oscillator systems causing the energy current power spectrum to saturate to a constant value at low frequencies is discussed. It is shown that a mode-coupling theory presented in earlier papers can be used to predict the frequency of onset of this finite-size effect. This can be used by researchers to plan simulations with large enough numbers of particles to avoid the presence of this finite-size effect.

Figure 1

Energy current power spectrum for a set of short runs ($N=2^{12},t_f=2^{18}$) and long runs ($N=2^{12},t_f=2^{18}$). Also shown are theoretical curves generated by the mode-mode coupling theory from Ref. [7]. These were generated from the short-run data using $n=2^{10},2^{12}$, and $2^{14}$. For comparison, the theoretical curve generated from the long runs is also shown.

Figure 2

Energy-current power spectrum for a set of long runs ($N=2^{14},t_f=2^{22}$) and a set of shorter runs ($N=2^{10},t_f=2^{22}$). Also shown are theoretical curves generated from the shorter runs using $n=2^{10}$ and $2^{12}$.