The superconducting properties in each point of the superconductor are described by the "complex" quantum mechanical wave function — the superconducting order parameter. As any complex function can be written as , where is the amplitude and is the phase. Changing the phase by will not change and, correspondingly, will not change any physical properties. However, in the superconductor of non-trivial topology, e.g. superconductor with the hole or superconducting loop/cylinder, the phase may continuously change from some value to the value as one goes around the hole/loop and comes to the same starting point. If this is so, then one has magnetic flux quanta trapped in the hole/loop, as shown below: