Structure of the output of the analysis program

Table 22: Structure of the <time>N<N>M<M>x-density.dat and <time>N<N>M<M>k-density.dat files.

Column $1$ to $3$	Column $4$ to $3+N_l$
$x,y,z$ or $k_x,k_y,k_z$	$\rho^i(x,y,z;t)$ or $\rho^i(k_x,k_y,k_z;t)$

These files are generated if Density_X/Density_K it true. $x,y,z$ and $k_x,k_y,k_z$ are the spatial and momentum grid, respectively, $N_l$ is the number of internal states, and $\rho^i(x,y,z;t)$ and $\rho^i(k_x,k_y,k_z;t)$ are the spatial and momentum densities, respectively. In the case of a computation treating atoms with internal structure, the index $i$ runs through all internal states of the considered atoms and one density is output for every state. In the names of the files <time> is the time $t$ <N> is the particle number, <M> is the orbital number.

Table 23: The nonescape probability output file Nonescape.

Column $1$	Column $2$
Time $t$	Nonescape probability $P_{not}(t,x_s,x_e)$

If the input variable Pnot and the borders $x_s$ and $x_e$ were defined with xstart and xend in the input of the analysis program, this file is created.

Table 24: Structure of the Entropy.dat file.

Column $1$	Column $2$	Column $3$	Column $4$
Time $t$	$S_{\rho-r}(t)=- \int d\vec{r}\rho(\vec{r};t) ln [\rho(\vec{r};t)]$	$S_{\rho-k}(t)=- \int d\vec{k}\rho(\vec{k};t) ln [\rho(\vec{k};t)$ ]	$S_C(t)= \sum_{\vec{n}} - \vert C_{\vec{n}}(t) \vert^2 ln [\vert C_{\vec{n}}(t) \vert^2 ]$

Column $5$	Column $6$	Column $7$
$S_n(t)= \sum_i - \frac{n_i(t)}{N} ln [\frac{n_i(t)}{N}]$	$I=\frac{1}{\sum_{\vec{n}} \vert C_{\vec{n}}(t) \vert^4}$	$S^N_C(t)= \sum_{\vec{n},\vec{n}'} - \vert C_{\vec{n}}(t) \vert^2 ln [\vert C_{\vec{n}'}(t) \vert^2 ]$

This file is generated when Entropy is set to true. The last column is only present if NBody_C_Entropy=.T. is set in analysis.inp.

Table 25: Structure of the TwoBody_Entropy.dat file

Column $1$	Column $2$	Column $3$	Column $4$
Time $t$	$S_{\rho^{(2)}-r}(t)=- \int d\vec{r}_1 d\vec{r}_2\rho^{(2)}(\vec{r}_1,\vec{r}_2;t)$ $ln [\rho^{(2)}(\vec{r}_1,\vec{r}_2;t)]$	$S_{\rho-k}(t)=- \int d\vec{k}_1 d\vec{k}_2\rho^{(2)}(\vec{k}_1,\vec{k}_2;t)$ $ln [\rho^{(2)}(\vec{k}_1,\vec{k}_2;t)]$	$S_{\rho_k^{(GO)}}(t)=\sum_i - \frac{\rho^{(GO)}_i(t)}{N} ln [\frac{\rho^{(GO)}_i(t)}{N}]$

. This file is generated when TwoBody_Entropy is true.

Table 26: Structure of the <time>N<N>M<M>x-correlations.dat and <time>N<N>M<M>k-correlations.dat files for multilevel computations.

Column $1$ to $3$	Column $4$ to $6$	Column $7+5(i-1)$	Column $8+5(i-1)$ & $9+5(i-1)$	Column $10+5(i-1)$
$x,y,z$ or $k_x,k_y,k_z$	$x',y',z'$ or $k'_x,k'_y,k'_z$	$\rho_i(x,y,z;t)$ or $\rho_i(k_x,k_y,k_z;t)$	$\rho_i^{(1)}(x,y,z\vert x',y',z';t)$ or $\rho_i^{(1)}(k_x,k_y,k_z\vert k'_x,k'_y,k'_z;t)$	$\rho_i(x',y',z';t)$ or $\rho_i(k'_x,k'_y,k'_z;t)$

Column $11+5(i-1)$

$\rho_i^{(2)}(x,y,z\vert x',y',z';t)$ or $\rho_i^{(2)}(k_x,k_y,k_z\vert k'_x,k'_y,k'_z;t)$

(For the explanation of the filenames, see table 22). These files are created, if the input variable Correlations_X and Correlations_K, respectively, are set to be true. The files contain all necessary quantities to compute the one-body as well as the diagonal of the two-body normalized (Glauber-) correlation function $g^{(1)}_i$ and $g^{(2)}_i$, respectively, for all internal states $i$. For instance, $\vert g^{(1)}_1\vert^2=\left\vert \frac{\rho^{(1)}_1(x_1,x'_1;t)}{\sqrt{\rho_1(x_1;t)\rho_1(x'_1;t)}} \right\vert^2$ can be plotted as the value of ( (Column $8$)$^2$ + (Column $9$)$^2$ ) divided by (Column $7$) $\times$ (Column $10$).

Table 27: Structure of the <time>N<N>M<M>x-correlations.dat and <time>N<N>M<M>k-correlations.dat files.

Column $1$ to $3$	Column $4$ to $6$	Column $7$	Column $8$ & $9$	Column $10$
$x,y,z$ or $k_x,k_y,k_z$	$x',y',z'$ or $k'_x,k'_y,k'_z$	$\rho (x,y,z;t)$ or $\rho (k_x,k_y,k_z;t)$	$\rho^{(1)}(x,y,z\vert x',y',z';t)$ or $\rho^{(1)}(k_x,k_y,k_z\vert k'_x,k'_y,k'_z;t)$	$\rho(x',y',z';t)$ or $\rho(k'_x,k'_y,k'_z;t)$

Column $11$

$\rho^{(2)}(x,y,z\vert x',y',z';t)$ or $\rho^{(2)}(k_x,k_y,k_z\vert k'_x,k'_y,k'_z;t)$

(For the explanation of the filenames, see table 22). These files are created, if the input variable Correlations_X and Correlations_K, respectively, are set to be true. The files contain all necessary quantities to compute the one-body as well as the diagonal of the two-body normalized (Glauber-) correlation function $g^{(1)}$ and $g^{(2)}$, respectively. For instance, $\vert g^{(1)}\vert^2=\left\vert \frac{\rho^{(1)}(x_1,x'_1;t)}{\sqrt{\rho(x_1;t)\rho(x'_1;t)}} \right\vert^2$ can be plotted as the value of ( (Column $8$)$^2$ + (Column $9$)$^2$ ) divided by (Column $7$)$\times$(Column $10$).

Table 28: Structure of the <time>N<N>M<M><x/k>corr<1/2>restr.dat files.

Column $1$ & $2$	Column $3$ & $4$	Column $5$	Column $6$
$x,x'$ or $k,k'$	$\rho^{(1/2)}(x\vert x';t)$ or $\rho^{(1/2)}(k\vert k';t)$	$\rho(x;t)$ or $\rho(k;t)$	$\rho(x';t)$ or $\rho(k';t)$

The generation of these files is triggered by the analysis input variables corr1restr,corr2restr,corr1restrmom,corr2restrmom. Similar to the above table 27, the normalized correlation functions $g^{(1)}$ and $g^{(2)}$ can be computed from the contents of these files, but for one-dimensional computations and on a restricted grid which is specified through the analysis input variables <x/k>ini<1/2>,<x/k>fin<1/2>,<x/k>pts<1/2>, respectively.

Table 29: Structure of the <time>N<N>M<M>x/k-order-<order>-correlations1D.dat

Column $1$ to $3$	Column $4$	Column $5$	Column $6$& $7$
$x,y,z$ or $k_x,k_y,k_z$	$\rho(x_{ref},y_{ref},z_{ref};t)$ or $\rho(k_{x,ref},k_{y,ref},k_{z,ref};t)$	$\rho (x,y,z;t)$ or $\rho (k_x,k_y,k_z;t)$	$\rho^{order}(\lbrace k_{x,ref},k_{y,ref},k_{z,ref}\rbrace,x,y,z;t)$ or $\rho^{order}(\lbrace k_{x,ref},k_{y,ref},k_{z,ref}\rbrace,k_{x},k_{y},k_{z};t)$

(For the explanation of the filenames, see table 22). These files are created, if the input variable anyordercorrelations_X and anyordercorrelations_K as well as oneD, respectively, are set to be true. The files contain all necessary quantities to compute the correlation functions up to order <order>. Here, $x_{ref}$/$y_{ref}$/$z_{ref}$/$k_{x,ref}$/$k_{y,ref}$/$k_{z,ref}$ correspond to the reference point specified in the input file by c_ref_x/c_ref_y/c_ref_z, respectively.

Table 30: Structure of the CorrelationCoefficient.dat file. This file is created when Correlation_Coefficient it true.

Column $1$	Column $2$ & $3$
time $t$	Real & imaginary part of $\tau=\frac{\langle x_1 x_2 \rangle-\langle x\rangle^2}{\langle x^2 \rangle-\langle x\rangle^2}$

Table 31: Structure of the <time>N<N>M<M>x-StructureFactor.dat files. These files are output if StructureFactor is true.

Column $1$ to $3$	Column $4$ and $5$	Column $6$ and $7$	Column $8$ to $10$	Column $11$ & $12$
$x,y,z$	Real and imaginary part of $\rho^{(2)}(\vec{r}_1=\vec{r}'_1=\vec{R},\vec{r}_2=\vec{r}'_2=\vec{r})$	Real and imaginary part of $\rho^{(1)}(\vec{r}_1=\vec{R},\vec{r}'_1=\vec{r})$	$k_x,k_y,k_z$	Real and imaginary part of dynamic structure factor $G= 1 + N \mathcal{F}$ $(\rho^{(2)}(\vec{r}_1=\vec{r}'_1=\vec{R},$ $\vec{r}_2=\vec{r}'_2=\vec{r}-1)$

Table 32: Structure of the lossops_N2_<border>.dat files.

Column $1$	Column $2$	Column $3$	Column $4$
Time $t$	$P_0^2(t)$	$P_1^1(t)$	$P_2^0(t)$

The generation of such a file is triggered by the lossops input variable being set to .T.. <border> is controlled by the border input variable. For each point in time $t$, a line in this file contains the probability $P_0^2(t)$ to find $2$ particles to the left of border, the probability $P_1^1(t)$ to find one particle to the left and one to the right of border, and the probability $P_2^0(t)$ to find two particles to the right of border.

Table 33: The structure of the <time>N<N>M<M><x/k><Slice 1>-<Slice 2>-correlations.dat files

Column $1$ to $4$	Column $5$	Column $6$	Column $7$ & $8$	Column $9$
$r_{1x},r_{1y},r_{2x},r_{2y}$	$\rho(\vec{r}_1;t)$	$\rho(\vec{r}_2;t)$	$\rho^{(1)}(\vec{r}_1 \vert \vec{r}_2;t)$	$\rho^{(2)}(\vec{r}_1 \vert \vec{r}_2;t)$

. These are output by the analysis program if the analysis input variable MOMSPACE2D or REALSPACE2D is set to .T.. <Slice 1/2> specify which cut through the real- or momentum-space density are in the file.

Table 34: The structure of the <time>N<N>M<M><x/k>-SkewCorrelations.dat files

Column $1$ and $2$	Column $3$	Column $4$ and $5$	Column $6$	Column $7$
$r_{1x},r_{1y}$	$\rho(\vec{r}_1;t)$	$\rho^{(1)}(\vec{r}_1 \vert -\vec{r}_1;t)$	$\rho(-\vec{r}_1;t)$	$\rho^{(2)}(\vec{r}_1, -\vec{r}_1;t)$

. These files are output of the analysis program if the analysis input variable MOMSKEW2D or REALSKEW2D is set to .T. .

Table 35: The structure of the <time>N<N>M<M><x/k>SingleShots.dat files

Column $1,2,3$	Column $4$ to $3+N_{shots}$
$x,y,z$	$N_{shots}$ samples of the $N$-body density

. These files are output of the analysis program if the analysis input variable SingleShot_Analysis or SingleShot_FTAnalysis is set to .T. .

Table 36: The structure of the <time>N<N>M<M><x/k>CentreOfMass.dat files

Column $1,2,3$	Column $4$
$x,y,z$	Histogram of $N_{samples}$ samples of the centre-of-mass-operator.

. These files are output of the analysis program if the analysis input variable CentreOfMass or CentreOfMomentum is set to .T. .

Table 37: The structure of the <time>N<N>M<M>phase.dat files.

Column $1$ to $3$	Column $4$	Column $5$ to $(5+M)$	Column $(6+M)$ & $(7+M)$	Column $(8+M)$ & $(9+M)$ to $(8+3M)$ & $(9+3M)$
$x,y,z$	$\xi _{avg}(x,y,z;t)$	$\xi _1(x,y,z;t)$ to $\xi _M(x,y,z;t)$	$\nabla _x \xi _{avg}(x,y,z;t)$ & $\nabla _y \xi _{avg}(x,y,z;t)$	$\nabla _x \xi _1(x,y,z;t)$ & $\nabla _y \xi _1(x,y,z;t)$ to $\nabla _x \xi _M(x,y,z;t)$ & $\nabla _y \xi _M(x,y,z;t)$

The generation of the files is toggled by setting the analysis input variable PHASE to .T.. If additionally GRADIENT it set to .T. then, Columns $(8+M)$ to $(9+3M)$ containing the phase gradients will be generated. Here $x,y,z$ are the coordinates, $\xi _{avg}(x,y,z;t)$ is the average phase, $\xi _1(x,y,z;t)$ to $\xi _M(x,y,z;t)$ are the $M$ orbital phases, $\nabla _x \xi _{avg}(x,y,z;t)$ & $\nabla _y \xi _{avg}(x,y,z;t)$ is the $x$ and $y$ component of the average phase's gradient, and $\nabla _x \xi _1(x,y,z;t)$ & $\nabla _y \xi _1(x,y,z;t)$ to $\nabla _x \xi _M(x,y,z;t)$ & $\nabla _y \xi _M(x,y,z;t)$ are the $x$ and $y$ components of the gradients of the $M$ orbital phases.