Superfluid Vortices & BKT Transition
Topological defects, vortex quantization, Berezinskii-Kosterlitz-Thouless unbinding
Parameters
Temperature T/T_BKT
0.80
Number of vortex pairs
4
Superfluid stiffness ρ_s
1.00
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Bound vortex pairs (superfluid)
T/T_BKT:
0.80
Bound pairs:
—
Free vortices:
0
ρ_s(T) ≈:
—
BKT transition:
In 2D superfluids/XY model, vortex–antivortex pairs bind below T_BKT and proliferate above it.
Quantization:
Circulation κ = nh/m, n ∈ ℤ. Vortex energy E ~ π ρ_s ln(R/a).
Universal jump:
ρ_s(T_BKT⁻) = (2/π) m kT_BKT (Nelson-Kosterlitz, 1977).