Solitons
A soliton is a self-reinforcing solitary wave that maintains its shape as it travels through a medium at a constant speed. Solitons arise via cancellation of nonlinear and dispersive effects in a gas or fluid.
In 1834, Scottish engineer John Scott Russell saw a solitary wave in a canal travel for over 8 miles without changing shape or amplitude. He then managed to reproduce solitons in a wave tank.
Solitons exhibit startling robustness in their coherence. Solitons can encounter each other and still maintain their integrity. Soliton dynamics vary depending upon the medium in which they appear.
A dark soliton is a standing dip in the density distribution of a medium; the opposite of a light soliton, which creates a wave of greater density than the surrounding medium.
Superfluidity – frictionless flow – arises in a Bose-Einstein condensate. Dark solitons can arise in a BEC.
Unlike bosons, fermions follow the Pauli exclusion principle, and so cannot occupy the same quantum state simultaneously.
To condense and form a superfluid, fermions must turn into bosons. They can do so by forming entangled pairs that have the requisite integer spin (each fermion has a half spin).
The size of an entangled fermion pair critically depends upon the interaction between pair members. An entangled pair may be tightly bound (a Cooper pair) or be at some distance. This determines the underlying physics of the condensate. Entangled pairs at a distance are relatively weakly bound, and yet more readily given to superfluidity.
A condensate may transition from close-knit to a greater inter-particle spacing or vice versa. In a condensate progressing to greater pair spacing, a dark soliton becomes more filled with non-condensed-gas atoms, making it heavier, and slowing it down.
This wave change occurs because quantum fluctuations have a more pronounced effect on the dark soliton. Solitons, which arise from coherence, are heavily influenced by the degree of fluctuations in the ground state.
