Vortex patterns emerge in quantum fields due to spin or disorder.Quantum vortices are whirlpool-like structures that appear in quantum fluids and fields, where circulation is quantized into discrete units. Unlike classical vortices (like a draining bathtub), these can only spin at specific, fixed rates, and their cores are typically regions where the quantum field's amplitude drops to zero. They emerge in systems ranging from superfluid helium and superconducting films to polariton condensates ('liquid light') and even hypothetical dark matter halos.
The concept was theoretically predicted by Lars Onsager in 1949 and independently by Richard Feynman in 1955, in the context of superfluid helium. Experimental confirmation came in the 1960s with experiments on rotating superfluid helium.
In a quantum fluid described by a complex wavefunction, the flow velocity is proportional to the gradient of the phase. For the wavefunction to remain single-valued, the phase change around any closed loop must be a multiple of 2π. This forces the circulation to be quantized: it can only take integer multiples of a fundamental quantum. At the vortex center, the phase is undefined, so the density must vanish, creating a 'hole' around which the fluid swirls. In superconductors, these vortices carry magnetic flux quanta and behave as particles that can form lattices, move, melt, or even serve as qubits.
Quantum vortices in superconductors are exploited in superconducting quantum interference devices (SQUIDs) for magnetometry, and are being explored as qubits for quantum computing. In polariton systems, they help study turbulence in quantum fluids.
In superfluid helium, a single quantum vortex carries exactly one quantum of circulation, about 10^-7 m²/s, which is so small that a typical vortex line would take thousands of years to complete one revolution if left alone.
| c_s | variable | sound speed — sound speed metre per second |
| P | variable | pressure of the scalar field — pressure pascal |
| X | variable | kinetic term, -1/2 (∂φ)^2 — kinetic energy density joule per cubic metre |
| P_X | variable | partial derivative of P with respect to X — partial derivative |
| P_XX | variable | second partial derivative of P with respect to X — second partial derivative |













