When a Superfluid Forgets Its Symmetry
04 May 2026, Yanjiang
Breaking Galilean invariance in a superfluid reveals a universal temperature-size scaling law validated by quantum simulations.
The physics of superfluids can seem almost too perfect. Cool certain liquids below a critical temperature and they lose all resistance to flow, slipping through tiny channels and climbing out of containers. The standard picture, taught for decades, explains this quiet degradation through something called a “phonon wind”—a gentle quantum breeze made of sound waves that picks up a tiny fraction of the liquid and carries it along. This breeze, and the temperature dependence it produces, rests on a single hidden assumption: that the fluid enjoys a deep symmetry known as Galilean invariance, a law that guarantees physics looks the same whether you glide with the flow or watch from the bank.
But whenever researchers try to understand what happens inside a porous sponge, an optical lattice, or a disordered solid—in short, wherever the pristine conditions of a free‑flowing superfluid are absent—the textbook account fails. A team of physicists at the University of Massachusetts Amherst has now uncovered why, and in doing so they have built a general theory that reveals a hidden universal behaviour.
Key facts from the study (arXiv:2605.00274):
- The classical Landau theory of superfluid depletion relies on a symmetry (Galilean invariance) that is broken when the fluid sits in a lattice or disorder.
- The researchers, Viktor Berger, Nikolay Prokof’ev and Boris Svistunov, derived a general formula for superfluid stiffness that does not require that symmetry.
- Their approach predicts a new scaling law that ties together the effects of temperature and system size, and it was validated by large‑scale quantum simulations.
- The theory resolves a decades‑old puzzle: why liquid helium trapped in Vycor glass shows a temperature dependence that contradicts Landau’s prediction.
- The work offers a practical framework for understanding superfluidity in real condensed‑matter systems, from high‑temperature superconductors to ultracold atomic gases.
In essence, the team has rewritten the low‑temperature thermodynamics of superfluids whose underlying symmetries are broken. What was once a mysterious anomaly becomes the signature of a different, equally universal law.
The ghost in the lattice
To appreciate what goes wrong, it helps to look at the original Landau idea from a more intuitive angle. Imagine a superfluid as a perfectly calm pond. The phonon wind is like a faint breeze rippling the surface, and in a free pond that breeze can travel unimpeded, carrying a tiny bit of the fluid’s momentum with it. Because Galilean invariance holds, the breeze alone accounts for the entire depletion of the superfluid component. The depletion itself changes with temperature in an extremely mild way—so mild that at the lowest temperatures it is almost undetectable. That is why, in a free superfluid, the loss of superfluid density behaves as if it receives an extra dose of protection from the cold.
Now place that pond inside a sponge, a crystalline lattice, or any environment that pins the fluid. The Galilean symmetry is no longer present. The phonon wind is still there, but it is no longer the whole story. Other collective excitations, and the way the fluid couples to the underlying structure, begin to matter. “The old picture is seductive because it works so cleanly in free space,” says Viktor Berger, the lead author of the study. “But once you break that symmetry, the depletion is not just a breeze—it becomes a whole weather system.”
Unlike a real weather system, however, these extra contributions are not random noise; they are governed by hidden constraints that the team’s analysis makes precise. This is not a matter of will, but a consequence of how quantum hydrodynamics responds to the breaking of a fundamental symmetry.
Finding order without symmetry
The team’s starting point was an elegant hydrodynamic action developed in the 1970s by the Russian theorist V. N. Popov—a framework that treats the superfluid as a field whose fluctuations encode both density and phase. That framework treats the superfluid as a field whose fluctuations encode both the density and the phase of the quantum condensate. When Galilean invariance is intact, several parameters in the action are forced to take specific values. Landau’s classic result, including its temperature dependence, drops out automatically. But if you allow those parameters to roam—because the fluid lives on a lattice, or because disorder scrambles the symmetry—something surprising happens.
Berger, Prokof’ev, and Svistunov calculated the superfluid stiffness directly from the action, keeping the anharmonic terms that normally get discarded. What they found is that the depletion of superfluid density follows a universal pattern even when Galilean invariance is gone, but the pattern is different. In a free Galilean system, the loss follows the familiar T⁴ law (in 3D). In a lattice or disordered system, the loss can be faster or even reverse sign—the stiffness may increase with temperature. Remarkably, the new law connects the finite‑temperature behaviour to the way the superfluid density responds to the mere size of the container. In a three‑dimensional sample, the effect of elongating the box becomes a mirror of the effect of warming it up: one tells you exactly about the other.
This duality, between temperature and scale, is the real treasure of the work. It means that an experimentalist who can measure the superfluid stiffness in a big sample at ultra‑low temperature can predict what will happen when the sample is made smaller, and vice versa. It is a kind of Rosetta Stone for superfluids that live in complex hosts.
The Vycor puzzle solved
The most striking confirmation comes from a classic set of experiments performed decades ago. Researchers had forced liquid helium‑4 into a sponge‑like glass called Vycor—a forest of nanometer‑wide pores—and had measured how the period of a torsional oscillator changed as the temperature dropped. The data stubbornly refused to follow Landau’s prediction. Instead of the extremely weak temperature dependence expected from a free superfluid, the oscillator showed a much steeper slope, hinting that something was eating away the superfluid mass faster than the phonon wind account could allow.
No fully satisfactory explanation emerged, and the result became a quiet puzzle in the literature. The new theory dissolves the puzzle. When the team digitised the old experimental curves from the 1980s and compared them with their predictions, the fit matched—with no free parameters. “The Vycor data are not an anomaly,” says Boris Svistunov, the principal investigator. “They are exactly what our formula requires when Galilean symmetry is broken by the porous glass.”
What makes this agreement powerful is that the formula contains no free knobs. All the parameters that enter it—the superfluid density at zero temperature, the speed of sound, the density of the liquid—are known independently. The theory simply computes the temperature dependence, and the old data fall on the line.
From the blackboard to the lattice
To be sure the mathematics was not a fluke, the team ran large‑scale quantum Monte Carlo simulations of a fundamental model: interacting bosons hopping on a two‑dimensional lattice at a fixed density. This model, known as the Bose‑Hubbard system, is a workhorse for studying superfluidity in optical lattices and solid‑state contexts. In the simulations, the superfluid stiffness was tracked as a function of temperature, and the results matched the analytical predictions with high precision. The simulations also confirmed that when the lattice spacing is made so large that the bosons are effectively isolated, the behaviour crosses over to the free‑space Landau result, exactly as the theory demands.
For the reader who enjoys a physical analogy, consider a river that has been forced to flow through a porous dam. In free water, the current’s resistance to disruption is the work of the water itself. But once the water threads through the dam, every pore constrains its motion, and the energy cost to move the liquid sideways changes. The river’s stubbornness is no longer a property of the water alone; it is a collective property of water‑plus‑dam. In the superfluid, the change from one power‑law behaviour to another is exactly that kind of re‑routing: the “sponge” of the lattice or disorder alters how the fundamental excitations sap the superfluid component.
A quiet revolution in measurement
These results do more than tidy up a long‑standing puzzle. They offer a practical lens through which to read future experiments. Many of the most exotic phases of quantum matter—high‑temperature superconductors, quantum spin liquids, and the crossover materials studied with ultracold atoms—are defined by how they break or preserve symmetries. The superfluid stiffness is a key observable in all of them, yet its interpretation has often relied on the Galilean‑invariant formula. The new framework from the UMass team shows that when the symmetry is absent, the natural variable to track is not simply a number describing stiffness; it is the scaling relationship that links size and temperature.
A torsional oscillator experiment that might have been puzzling can now be understood as a clean window into the symmetry class of the system. If an experiment reveals a temperature dependence that matches the broken‑symmetry scaling, it sings the song of a lattice. If it matches the older, milder dependence, the system remains effectively free.
From a larger perspective, the preprint (arXiv:2605.00274) is a reminder that symmetry—so often treated as a sacred principle—can sometimes blind us to distinct yet equally universal behaviours. When it is broken, nature does not fall into chaos; it finds new organizing principles. For physicists who study correlated materials, this work may become a standard tool: a way to decode the whispers of a superfluid that dances to a different tune. That dance is not born of choice, but of the deep structure of quantum fields confined by a host that refuses to grant them the freedom of empty space.
Yanjiang is an online editor of Loom Science
References
- Viktor Berger et al., Low-temperature Depletion of Superfluid Density in the Absence of Galilean Symmetry, arXiv:2605.00274