Periodicities in a multiply connected geometry from quenched dynamics

Exploring the lowest energy configurations of a quantum system is consistent with the counting statistics of the frequently appeared states from quenching dynamics. By studying the Little-Parks periodicities in a multiply-connected ring-shaped geometry from the holographic technique, it is found that the frequently appeared states from dynamics incline to have lower free energies. In particular, the resulting winding numbers from quenched dynamics are constrained in a normal distribution for a fixed magnetic flux threading the ring. Varying the magnetic fluxes, Little-Parks periodicities will take place with periods identical to the flux quantum $\Phi_0$. Favorable solutions with lowest free energies perform first order phase transitions which transform between distinct winding numbers as the magnetic flux equals half-integers multiplying $\Phi_0$.