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.


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