Persistent Current in a Mesoscopic Ring

When a normal-metal or semiconductor ring is cooled below the point where its circumference is shorter than the electron's phase-coherence length, its ground state carries a real, non-decaying circulating current whenever a magnetic flux threads the loop — a striking consequence of single-particle quantum coherence with no analogue in classical circuit theory. This simulator builds a physically grounded model of that persistent current: single-particle levels E_n(Φ) = (ħ²/2mR²)(n − Φ/Φ₀)² are filled with N electrons, the total energy is differentiated with respect to flux to get I(Φ), and the result is rendered as flowing current markers around a 3D ring with a visible flux tube through its center, alongside a live flux-periodic sawtooth strip chart. Sliders let you sweep the threaded flux, change the electron count to see the even/odd parity effect flip the current's sign, resize the ring to change the energy scale, and dial in dephasing to watch the effect wash out — reproducing the real behaviour measured in isolated mesoscopic gold and GaAs rings.