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To use discrete fast-Fourier transformation to compute the integrals over ω and t, we have to set a typical stepsize in frequency to be much smaller than ex and ey and the pinning peak widths. These quantities are dependent on the disorder level. On the other hand, the frequency stepsize is inversely proportional to the large- t cutoff. As the depinning transition is approached and in the depinned state that we will discuss in Sec. 6, to see all the interesting features at small ω we need to use very large cutoff. We thus need to compromise on the disorder level in order to capture the interesting physics at low frequencies.
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We want to mention that the weight of this delta function term is not computed accurately in the current method since this term has to be obtained along with the ωn =0 mode of ζ.
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We want to mention that the weight of this delta function term is not computed accurately in the current method since this term has to be obtained along with the ωn =0 mode of ζ.
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