Simplest Live Demonstration of Adiabatic Transport I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original position then the phase changes. I was thinking about a moving a simple spinning wheel, but I have trouble matching two wheels to rotate in the same frequency and phase to compare them after one experiences adiabatic transport. Both wheels did not have the same friction coefficient.
 A: I think that for a reliable demonstration of the spinning wheel system,  a design using bearings would be essential, in order to achieve frictionless reactions. 
A demonstration can be achieved by means of the linear planimeter , which measures areas enclosed by plane curves, by measuring a rotation angle of its wheel. 
I think that a planimeter model can be built by elementary means. Please see, the following elementary description by: Tanya Leise.
The planimeter returns to its original state after its tracer end completes a full turn around the closed curve, only its wheel acquires a net rotation which is a Berry phase proportional to the traced area.
In fact an elementary application of Stokes theorem shows that the area of closed planar curve $\mathcal{C}$ can be written as a Holonomy of an artificial gauge field:
$$ Area = \int_{\mathcal{C}} \frac{1}{2}(x dy - y dx) =  \int_{\mathcal{C}} \mathbf{A} \cdot  d \mathbf{r}  = \int_{\mathcal{C}}  \mathbf{\nabla}\times \mathbf{A} \cdot \mathbf{n_z} dS$$ Where, the artificial gauge field:
$$ \mathbf{A }= \frac{1}{2}\{-y , x, 0\}$$
It's corresponding "magnetic field"
$$ \mathbf{B }=  \mathbf{\nabla}\times \mathbf{A}  =  \{0 , 0, 1\}$$
Thus
$$ Area = \int_{\mathcal{C}}  B dS =  \int_{\mathcal{C}} dS $$
