Pancharatnam Phase of a Mesoscopic Coupled Circuit

We derive a formula of the nonadiabatic noncyclic Pancharatnam phase for a mesoscopic circuit with coupled inductors and capacitors. It shows that,because of coupling effect, the circuit is in squeezed quantum state initially, and the time evolution of Pancharatnam phase exhibits an oscillation in a complex way. Especially we findthat when the capacity of the coupled capacitors is larger thanthat of other ones in the circuit, with the variation of time Pancharatnamphase becomes nearly periodic square-wave, which perhaps can providea new approach for the realization of quantum logic gate.