Electron gas turns out to be as finicky as ketchup ✛ ✎ ✦

Original: "Non-Newtonian two-dimensional electron fluid in magnetic field"
· P. S. Alekseev, M. A. Semina
arXiv:2606.27788 · 2026-06-26 · arXiv non-exclusive · independent analysis · 1 min
Electric current in an ultrapure crystal thickens or thins like ketchup — it all depends on the flow speed.

Electrons in ultrapure crystals stop being a swarm of particles — they flow like a liquid. This picture was proposed back in the mid-20th century by Landau. However, recently physicists noticed: in a strong magnetic field, the resistance of this electron gas changes in jerks, as if the liquid alternately freezes and thins. The reason is that the current heats the flow unevenly — in the middle of the channel, where the speed is higher, viscosity changes more. According to numerical models, in a weak field, the electron ketchup becomes thinner when accelerating. But in a strong field — it first hardens, like wet sand, and then thins even more than before. The same mechanism governs matter in white dwarfs, where an increase in entropy leads to similar viscosity jumps. It was these jumps that Boltzmann once explained through the tendency toward disorder. This discovery overturns the view of quantum fluids — it turns out that the laws of Newton are powerless here. And in the future, such nonlinear effects will help create ultrasensitive magnetic sensors and, perhaps, control magnetic processes in electron flows.

Non-Newtonian fluids are familiar to everyone: ketchup that won't pour out of the bottle until you shake it, and wet sand that hardens upon impact. Now, the two-dimensional electron gas in a magnetic field has officially joined this list — physicists have confirmed that it too gets finicky.

\eta_{xx}^{\mathrm{nl}} = \frac{\eta_0}{h + \beta^2/h}, \quad h = 1 + \tau_{2,ee}^{(0)} \tau_{\Delta} G^2
The nonlinear viscosity depends on the velocity gradient G and the magnetic field via the parameter β. For β<1 it decreases with G (pseudoplasticity), for β>1 it behaves nonmonotonically: first rises, then falls (dilatancy with a kink).
\alpha (T_e - T_{\mathrm{ph}}) = m \eta_{xx} \left( \frac{dV}{dy} \right)^2
Heat balance in the electron fluid: the left side is the energy outflow to phonons, the right side is the Joule heating due to viscous friction. This equation closes the self-consistent problem and determines the local temperature.
Scientists
Ludwig BoltzmannRudolf ClausiusSatyendra Nath BoseJohn BardeenFelix BlochGeorg Ohm
Concepts
non newtonian fluid hydrodynamics Poiseuille's equation electrolyte transport Faraday's law of electromagnetic induction electron liquid solid electrolyte fluid flow conduction electron reynolds number spin current magnetic dynamo heat flow magnetic energy superfluidity anomalous hall effect Bernoulli's principle magnetic field Poynting's theorem smoothed particle hydrodynamics