Condensed Matter Ep 5: Superfluids

Stand a glass beaker in a bath of liquid helium below about two kelvin, rim well clear of the surface, and it empties itself. Uphill, over its own rim, through a film thirty nanometres thick — a hundred atoms deep, coating every surface in the cryostat. Nothing pumps and nothing pushes, and it does not stop until the beaker is dry. The previous conversation built Landau's wine-bottle trough and the stiffness that comes with it. This one spends that stiffness. The claim to be earned is precise, and it is not the one most people carry: superflow is not frictionless by magic, it is *metastable* — the fluid cannot find a way to lose momentum in small enough pieces, so it keeps it. The argument is Landau's and it is one line of geometry. Draw the excitation spectrum, draw a straight line from the origin, and the slope of the steepest line that still touches the curve is the fastest the liquid can flow without being able to shed anything at all. A free particle's spectrum bends away from the origin like a parabola and that line has zero slope — an ideal Bose gas is not a superfluid, which is the first surprise. Interactions are what lift the curve into a straight rise at small momentum, and the straight rise is what buys the critical velocity. Then the second surprise: helium's measured critical velocities are far *below* Landau's number, because vortices nucleate at rough patches long before rotons do, and the honest version of the theory is the one that says so. Also: why the wavefunction's phase must return to itself around a loop, and how that single requirement forces circulation to come in whole units rather than any amount; the two-fluid picture and Andronikashvili's stack of discs in Kapitza's Moscow institute, which weighed the normal fraction directly; the roton minimum and what it is a memory of; why only about nine per cent of helium-four is in the condensate while all of it flows, so "condensate" and "superfluid" are not the same word; Gross–Pitaevskii assembled from Schrödinger plus one term; Kapitza coining "superfluid" in the last sentence of his paper, by analogy with superconductors; and the cold gases, where the same physics can be ordered to specification — including the two clouds released to overlap and interfere, a year and a half after the first condensates. The closing strand is helium-three, which has to pair before it can do any of this: fermions with no charge, a complicated order parameter, and thirty years between the question and the answer. Next time the particles that pair are charged, and one number — a factor of two in a measured flux — proves it. ——— Series: Physics - Tutorial · Grad level. Every equation spoken in full, no chalkboard required. Built by Fermi AI.