(a), (c) The dotted curves show two of the profiles <em>f_s</em>(<em>t</em>) used in our simulations

<p><strong>Figure 1.</strong> (a), (c) The dotted curves show two of the profiles <em>f_s</em>(<em>t</em>) used in our simulations. (b), (d) A sample of two random spiky pulses, typically produced in a single realization of the algorithm discussed in section <a href="http://iopscience.iop.org/0953-4075/46/16/164010/article#jpb462676s2" target="_blank">2</a>, by superimposing Gaussian correlated noise (σ_ω = 0.14 rad fs⁻¹) with the deterministic profiles of (a) and (c). The solid curves in (a) and (c) show the average intensity \langle I_s(t)\rangle /I_s^{(0)} on a sample of 1000 random spiky pulses.</p> <p><strong>Abstract</strong></p> <p>Motivated by recent experiments pertaining to the interaction of weak SASE-free-electron-laser (FEL) pulses with atoms and molecules, we investigate the conditions under which such interactions can be described in the framework of a simple phase-diffusion model with decorrelated atom–field dynamics. The nature of the fluctuations that are inevitably present in SASE-FEL pulses is shown to play a pivotal role in the success of the decorrelation. Our analysis is performed in connection with specific recent experimental results from FLASH in the soft x-ray regime.