Dear All,

I was consulting the example of the current in a closed system and I am a little bit confused:

The figure showing the current flowing inside a circle [1] is obtained for a magnetic field B=0 !

But we know that for B=0, the Hamiltonian is a real symmetric matrix and thus diagonalized by a real orthogonal matrix, so the eigenvectors are real (any phase is just artificial.)

By using the formula giving the current we should find zero !

moreover we can ask why we have a current flowing clockwise and not anticlockwise (I remind that B=0) !

When we put B=0.05,  we obtain  the figures below for the current and the wave function.

the wave function has circular symmetry but not the current. Moreover, x and y play exactly the same role so the current should be the same on x and on y (independently from the used gauge)

Am I missing something ?