## Convergence of the algorithm discussed in section 2

**Figure 3.** Convergence of the algorithm discussed in section 2. The modulus of *g*^{(1)}(*t*, *t*') is plotted as a function of *t* − *t*'. Averaging over a large number of pulses (trajectories), |*g*^{(1)}(*t*, *t*')| converges to equation (12) (grey thick line). Other parameters: τ = 10 fs, σ_{ω} = 0.25 rad fs^{−1}.

**Abstract**

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.