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I want to represent parallel transport as in the following figure, but next to this figure I would like to place a diagram with the two arrows (of the initial state and of the final state that are present at the top of the spherical surface) and the angle between them, to see better and put more emphasis on the analogy with the Berry phase.

How can I draw the two arrows and the angle? Is there a program that allows me to do this and is free? What programs do you use to draw images from scratch and are free (and provide good images for example, to put in articles)?

The image was taken from this thesis.

enter image description here

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The figure you are showing can be made in Adobe Illustrator or Gimp

I've recreated a crude rendition (very quickly) using adobe illustrator

enter image description here

The steps to get this far are:

  1. create a sphere
  2. cut the sphere in half with pathfinder divider tool
  3. Revolve the half sphere with the 3d effect
  4. in the revolve menu select Wireframe surface
  5. in the revolve menu select map art (this is how I got the blue colors to add). I used the process rectangle "symbol". I used two surfaces, the 1st and 4th. because those showed up how I wanted them too (I'm not sure if this is the best way).

The arrows can be added in and "revolved and beveled" to get them in the proper orientation.

For more information you should probably seek help on the Adobe illustrator Stack Exchange.

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