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BProbeM, a fuzzy quantum geometry scanner, is a Wolfram Mathematica package. It is the implementation of an algorithm which rasterizes the semi-classical limit of a fuzzy brane described by a set of matrices.
BProbeM is a fork of BProbe, adding several features for scanning such as the newly added directional scans, improves and completes missing documentation and improves typical scenario computation times by changing how some internal procedures are handled.
The underlying theory is not described in this documentation, and for a comprehensive treatment is referred to the paper introducing the original BProbe.
How to install and use this package is described in Installation & Getting-Started.
The methods constituting this package can be divided into four categories:
- Initialization
- Directional scanning in preparation for the 'actual' scan
- 'Actual' scanning using quasi-coherent state algorithm
- Helper functions
-
ProbeGetOperator(example) -
ProbeGetGroundstateEnergy(arguments, example) -
ProbeGetEnergies(arguments, example) -
ProbeGetGroundstate(arguments, example) -
ProbeGetGroundstates(arguments, example) -
ProbeGetExpectedLocation(arguments, example) -
MatrixRepSU2(arguments, example) -
MatrixRepSU3(arguments, example)
-
ProbeScan is the primary scanning utility. It implements the algorithm to rasterize the semi-classical limit of the brane configuration defined by a set of matrices as submanifold of the target space 
ProbeGetPoints. Optionally, information about their tangent spaces is obtainable via ProbeGetTangentspaces.
The commands ProbeDirectionalScan, ProbeGetDirectionalData, ProbeShowDirectionalPlot are used for preliminary directional scanning which is very useful for helping with the appropriate selection of starting points and parameters in preparation for the actual scan. Getting familiar with this procedure will be crucial for the sensible use of the package on non-trivial examples. On trivial examples, ProbeScan can manage on its own, but with more complicated structures manual focusing can increase scan quality quite drastically.
The commands ProbeGetOperator,ProbeGetGroundstateEnergy, ProbeGetEnergies, ProbeGetGroundstate, ProbeGetGroundstates and ProbeGetExpectedLocation are helper functions which have nothing to do with the actual scanning procedure. However, they can be used to get specific information of certain points in the target space
Before the methods with the Probe prefix can be used, the package has to be initialized by calling the method ProbeInit.
In addition, this package provides matrix representations of SU(2) and SU(3) through the methods MatrixRepSU2 and MatrixRepSU3 for convenience, since they exhibit a class of more or less well known fuzzy branes.
For a detailed description of the methods and examples please visit the associated Wiki-pages. They are accompanied with small examples. Two larger examples that go through a typical application process including the thought process of BProbeM are provided in the Examples-section.
See the attached Wolfram Mathematica notebook on the Fuzzy 2-sphere (Right Click + Save As).
See the attached Wolfram Mathematica notebook on GUE matrices (Right Click + Save As).
As an additional service for learning how to use this package, we include a sort of "exercise" notebook here as well. In this notebook we will provide a set of matrices and it is up to you to study its semi-classical limit. Remember: The challenge is to understand the structure of an unknown matrix geometry, so try to approach it as such. To do the exercise without help, simply copy the initialization matrix set at the top of the notebook and explore the provided 'special' matrix geometry yourself.
See the attached Wolfram Mathematica notebook including step by step help (Right Click + Save As).