ABSTRACT
In previous chapters, we saw that the most quintessential properties of superfluids and superconductors are described by the classical complex scalar field. These properties are universal and robust in the sense that they are independent of the microscopic origin of the classical field and insensitive to the presence of disorder. In single-component systems, several effects are considered to be the hallmarks of superfluidity. One of them is the quantization of superfluid-velocity circulation with the circulation quantum depending only on the microscopic parameter γ (recall that, in a quantum system, γ is directly related to the bare particle mass: γ = /m). Another example is the Onsager-Feynman relation (1.187) between the density of rotation-induced vortices and angular velocity, with γ being the only system-specific parameter entering the expression. In a single-component superconductor, an even more impressive universality takes place in the context of magnetic flux quantization: With quantum field theory taken into account, the magnetic flux quantum turns out to be a ratio of fundamental constants only-the particle mass drops out: Φ0 = πc/e. The extraordinary robustness of those phenomena is dictated by topology-quantization of the phase gradient circulation for the (coarse-grained) complex field.
