Geometric phase in Bohmian mechanics

Abstract

Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2 π. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov–Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.