phenomenological constants, which can potentially be fixed by comparison with measured observables.

At the [*microscopic*]{} level the physical scale of the order of fermi (fm$=10^{-13}$ cm) is set by the nuclear forces. The long-range attractive interaction between nucleons leads to an instability of the normal state of the nuclear matter against Cooper pairing, in analogy to the microscopic Bardeen-Cooper-Schrieffer theory of superconductivity of metals. The nuclear forces control the size of the “elementary bosons” of the theory - the Cooper pairs, which appear as weakly bound states of two fermions near the Fermi surface. The size of a Cooper pair, the [*coherence length*]{} $\xi$, is of the order of 10 fm. It sets, obviously, the lower scale on which the hydrodynamic description of superfluids breaks down. On length scales larger than $\xi$, the condensate of Cooper-pairs can be described by a single wave function $\psi({\bf x})$, i.e., the condensate forms a macroscopically coherent state.

At the [*local hydrodynamic*]{} level the relevant physical scale is set by the size of vortices - macroscopic quantum objects, whose fundamental property is the quantization of the circulation around a path encircling their core. The circulation is quantized in units of $2\pi\hbar$ since the condensate 