Superfluid Density in Pairing Theory of Superfluidity
It has long been recognized that the question of whether a system is superfluid or not may be formulated in terms of the properties of its linear response kernel, for such a kernel can tell us what the ultimate state of a system, initially in uniform motion relative to some weak scattering mechanism (walls, etc.), will be. If this final state should possess a nonvanishing current density (measured relative to the walls), then we say the system is superfluid and the magnitude of the residual current density relative to the initial current density defines the superfluid density relative to the density. More precisely, if we imagine a system at rest relative to some weak scattering mechanism, and at time t = 0 we impart to each atom in the system a small impulse such that its velocity is increased by a small amount v s , then the initial current density (t = 0+) will be j(0+) = ρv s .
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