Question

Is it possible to change one quantum state to another state by a cyclic adiabatic process?

Answer 1

An alternative definition of a reversibleprocess is a process that, after it has taken place, can be reversed and, when reversed, returns the system and its surroundings to their initial states. In thermodynamic terms, a process"taking place" would refer to its transition from one state to another.

Answer 2

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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 CC can be written as a Holonomy of an artificial gauge field:

Area=∫C12(xdy−ydx)=∫CA⋅dr=∫C∇×A⋅nzdSArea=∫C12(xdy−ydx)=∫CA⋅dr=∫C∇×A⋅nzdS

Where, the artificial gauge field:

A=12{−y,x,0}A=12{−y,x,0}

It's corresponding "magnetic field"

B=∇×A={0,0,1}



Area=∫CBdS=∫CdS


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