In the standard Little-Parks experiment the critical temperature of a cylindrical superconductor oscillates with the magnetic flux that threads the system. However, a recent experiment has demonstrated that when the cylinder diameter is reduced to the superconductor correlation length, the flux can drive the system into the normal state. The root cause of this effect remains an open question as until now it has not been possible to calculate the current flow through a superconductor in the presence of disorder, magnetic field, interactions, finite current, and finite temperature.

Here we develop a new tool to calculate the exact current flow, that starts from a microscopic model, and accounts for both the phase and amplitude fluctuations in the superconducting order parameter. We first validate the formalism against well-established phenomena in mesoscopic systems, and secondly address the long-standing mystery surrounding the quantum Little Parks effect.