this case the amplitudes of its Fourier modes fulfill Eq. .

![Top: Fourier mode amplitudes of a thermally equilibriated dislocation against wave number; dashed line: $A_n^2 \propto n^{-2}$ as expected for an elastic line according to ; bottom: effective line energy as determined from , full: guide to the eye.\[fig:eqdis\]](eqdis.pdf){width="3.3in"}

The amplitudes of the Fourier modes of the equilibrated dislocation are shown in Figure \[fig:eqdis\], top. We observe that, for short wavelengths (large wave numbers), characteristic deviations occur from the $A_n^2 \propto n^{-2}$ behavior expected according to Eq. \[fig:eqdis\]. Of course, in our simulations the self-interaction of a dislocation line is described by a non-local interaction kernel which is much more complex than a simple elastic line. So the question arises whether we can understand the deviations and quantify them.

To this end, we first use to determine a wave number dependent line energy. This is shown in Figure \[fig:eqdis\], bottom. We can see that, for long-wavelength fluctuations, the data can be well described by an approximately constant line energy. However, on short scales (large wave numbers) the effective line tension seems to be decreasing. To understand this behavior, we have, in Appendix A, calculated the Fourier transform of the 