The Boltzmann distribution and molecular gases

“The Boltzmann distribution and molecular gases” explains why an “ordinary” gas has its molecules Boltzmann-distributed. The most concentrated Fermi–Dirac gas, helium 3 at its boiling point, is still in a “dilute limit”, dilute enough to be approximately Boltzmann. Similarly, the most concentrated Bose–Einstein gas, helium 4 at its boiling point, is also approximately Boltzmann.

Bubbles in superfluid helium containing six and eight electrons: Soft, quantum nanomaterial

The role of quantum fluctuations in the self-assembly of soft materials is relatively unexplored, which could be important in the development of next-generation quantum materials. Here, we report two species of nanometer-sized bubbles in liquid helium-4 that contain six and eight electrons, forming a versatile, platform to study self-assembly at the intersection of classical and quantum worlds. These objects are formed through subtle interplay of the short-range electron-helium repulsion and easy deformability of the bulk liquid. We identify these nanometric bubbles in superfluid helium using cavitation threshold spectroscopy, visualize their decoration of quantized vortex lines, and study their creation through multiple methods. The objects were found to be stable for at least 15 milliseconds at 1.5 kelvin and can therefore allow fundamental studies of few-body quantum interactions under soft confinements.