Quantum Vortices Flow Through a Superconductor Under AC Current

Twelve quantized magnetic vortices evolve through a two-dimensional type-II superconductor while an alternating transport current drives the system through six complete cycles. This simulation solves a two-dimensional time-dependent Ginzburg-Landau equation for the complex superconducting order parameter \(\psi(x, y, t)\) : \[ u\left(\frac{\partial}{\partial t}+i \phi\right) \psi=(\nabla-i \Lambda)^2 \psi+\left[\epsilon(x, y)-|\psi|^2\right] \psi . \] The magnitude \(|\psi|^2\) gives the local condensate density. A magnetic vortex is a true zero or near-zero of this field around which the phase winds by \(2 \pi\). The production run begins with 12 positive vortices in an applied field \[ B=0.0245437, \] corresponding to 12 applied flux quanta across the film. The sample contains 22 static material pinning defects with three strengths, represented directly through the spatial coefficient \(\epsilon(x, y)\). The transport current is \[ J_{\text {drive }}(t)=J_{\mathrm{ac}} \sin \left(\frac{2 \pi t}{T_{\text {drive }}}\right) \] with \[ J_{\mathrm{ac}}=0.1456, \quad T_{\text {drive }}=220 . \] Six complete cycles are followed continuously, with no reset of the superconducting field between cycles. The video shows: The actual calculated complex superconducting order parameter Quantized magnetic vortex cores A static material-pinning landscape Six complete AC-current cycles Strong vortex motion and vortex-vortex interactions Changing pin occupancy and boundary exits Voltage generated during flux flow Current-voltage hysteresis Fourier-space sonification of the same complex field The gauge-invariant superconducting current is \[ \mathbf{J}_s=\operatorname{Im}\left[\psi^*(\nabla-i \mathbf{A}) \psi\right] . \] Charge conservation is enforced through \[ \nabla \cdot \mathbf{J}=0 . \] The simulation uses the fixed Landau gauge \[ \hat{\mathbf{A}}=(-B y, 0), \] with gauge-covariant link variables so the magnetic field enters the numerical derivatives consistently. Vortex trajectories are never prescribed. Vortices are detected from gauge-covariant phase winding of \(\psi\) and then tracked through time. The mobile-vortex fraction reached 1.0 , while the maximum mean tracked vortex speed was approximately 0.172 in simulation units. Four vortices physically exited the simulated film during the six-cycle trajectory, so the detected vortex count changed from 12 initially to 8 at the end. These losses were not inserted or animated; they emerged from the TDGL evolution. The electrical response also evolved strongly. The peak measured voltage was approximately \[ V_{\max }=0.403, \] and the current-voltage loop had a hysteresis area of approximately 0.819 in dimensionless units. The main three-dimensional camera displays the actual calculated order parameter. The horizontal plane is the superconducting film, surface height represents a fixed global transformation of \(|\psi|^2\), and color represents \(\arg \psi\) in the chosen gauge. The visible vortex holes are therefore features of the numerical field itself. Unlike the unitary quantum-wavefunction simulations in this series, time-dependent Ginzburg-Landau evolution is dissipative. The norm of \(\psi\) is not expected to be conserved. Validation instead includes gauge covariance, current conservation, zero-drive free-energy relaxation, vortex winding, spatial convergence, timestep convergence, and trusted-field identity. The production calculation used a \(64 \times 48\) domain with spatial step 0.25 , timestep 0.01 , and \(u=5.79\). The maximum discrete current-divergence residual was approximately \(2.75 \times 10^{-14}\). Gauge-current and gauge-Laplacian tests agreed to approximately \(5.0 \times 10^{-16}\) and \(4.6 \times 10^{-15}\), respectively. The model is a phenomenological dirty-limit TDGL description of an effectively two-dimensional type-II superconducting film. The external magnetic vector potential is prescribed; magnetic self-fields, thermal noise, microscopic quasiparticles, quantum vortex tunneling, and heating feedback are not included. The accompanying audio is not literal sound from the superconductor. It is a mathematical sonification of the spatial Fourier spectrum of the same complex order parameter, \[ P(\mathbf{k}, t)=|\mathcal{F}[\psi(x, y, t)]|^2 . \] Moving magnetic flux is one of the central sources of dissipation in practical type-II superconductors. Here the pinning landscape, vortex motion, boundary losses, and electrical response all emerge from one evolving complex field. #Superconductivity #QuantumVortices #TypellSuperconductor #GinzburgLandau #FluxFlow #VortexPhysics #CondensedMatterPhysics #QuantumPhysics #ScienceVisualization