A universal scaling of condensation temperature in quantum fluids

Abstract

The phenomena of superconductivity and superfluidity are believed to originate from the same underlying physics, namely the condensation of either bosons or pairs of fermions (Cooper pairs). In this work I complied and analyzed literature data for a number of quantum fluids and showed that indeed they all follow the same simple scaling law. The critical temperature for condensation T$_c$ is found to scale with the condensate coherence length $\xi$ and the effective mass of condensing particles m$^{\ast}$. The scaling plot includes members of most known classes of superconductors, as well as a number of superfluids and condensates, such as $^3$He, $^4$He, dilute Bose and Fermi gases, excitons, polaritons, neutron superfluid and proton superconductor in neutron stars, nuclear pairing, quark--antiquark condensate and Higgs condensate. The scaling plot spans more that 24 orders of magnitude of critical temperatures, albeit the scaling exponent is not the one predicted by theory. The plot might help the search for a QCD axion.