deletions | additions       diff --git a/Photoemission.tex b/Photoemission.tex  index 0f50cf4..ff7453b 100644  --- a/Photoemission.tex  +++ b/Photoemission.tex 
...
imposes periodic boundary conditions that spuriously reintroduces charge that was supposed to disappear.  This is illustrated with a one dimensional example in Fig.~\ref{fig:pes_nfft}~(a) where a wavepacket  launched towards the left edge of the simulation box reappears from the other.  \begin{figure}[h!]  \begin{center}  \includegraphics[width=\columnwidth]{figures/nfft_discretization/nfft_discretization.eps}  \caption{\label{fig:pes_nfft}  Scheme illustrating different discretization strategies for Eq.~\eqref{eq:FMM_prop_aux} in one dimension.  In all the cases an initial wavepacket (green) is launched towards the left side of a simulation box of   length $L$ and discretized in $n$ sampling points spaced by $\Delta x$. $A$ and $B$ indicate the   space partitions corresponding to Fig.~\ref{fig:pes_sheme}.  Owing to the discretization of the Fourier integrals periodic conditions are imposed at the boundaries and  the wavepacket wraps around the edges of the simulation box (red).   The time evolution is portrayed together with a momentum space representation (yellow), with spacing $\Delta k$  and maximum momentum $k_{\rm max}$, in three situations differing in the strategy used to map real and  momentum spaces:(a) Fast Fourier transform (FFT), (b) FFT extended with zeros (zero padding) in a box enlarged   by a factor $\alpha$, and (c) zero padding with NFFT.   }  \end{center}  \end{figure}  An alternative discretization strategy is that of using zero padding.   This is done by embedding the systems into a simulation box enlarged by a factor $\alpha>1$, extending