Three-Dimensional Low-Density Fermions in Planckian Limit: Entropy and Dynamics

In this Letter, we explore dynamics in a three-dimensional strongly interacting liquid. In quantum liquids discussed below, thermodynamic properties such as pressure and thermal energies are fully characterized by $s(T)$, the entropy density of the liquid (that is also directly proportional to the hydrodynamic viscosity). We obtain a universal fermion spectral function $A(\omega ,\mathbf{k})$ that is distinctly specified by $\mathrm{\hslash }\mathrm{/}T$, a Planckian time scale. These phenomena can emerge in strongly interacting many-body states with a finite fermion density $\rho$ at temperatures $T^{\ast }$ where the chemical potential of fermions $\mu (\rho ,T=T^{\ast })$ approaches zero and can be thought as many-body simulations of certain aspects of Planckian dynamics.