Universal lower bounds on energy and momentum diffusion in liquids
Kostya Trachenko, Matteo Baggioli, Kamran Behnia, В. В. Бражкин
Abstract
Thermal energy can be conducted by different mechanisms including by single particles or collective excitations. Thermal conductivity is system-specific and shows a richness of behaviors currently explored in different systems, including insulators, strange metals, and cuprate superconductors. Here, we show that despite the seeming complexity of thermal transport, the thermal diffusivity $\ensuremath{\alpha}$ of liquids and supercritical fluids has a lower bound that is fixed by fundamental physical constants for each system as ${\ensuremath{\alpha}}_{m}=\frac{1}{4\ensuremath{\pi}}\frac{\ensuremath{\hbar}}{\sqrt{{m}_{e}m}}$, where ${m}_{e}$ and $m$ are electron and molecule masses. The newly introduced elementary thermal diffusivity has an absolute lower bound dependent on $\ensuremath{\hbar}$ and the proton-to-electron mass ratio only. We back up this result by a wide range of experimental data. We also show that theoretical minima of $\ensuremath{\alpha}$ coincide with the fundamental lower limit of kinematic viscosity ${\ensuremath{\nu}}_{m}$. Consistent with experiments, this points to a universal lower bound for two distinct properties---energy and momentum diffusion---and a surprising correlation between the two transport mechanisms at their minima. We observe that ${\ensuremath{\alpha}}_{m}$ gives the minimum on the phase diagram except in the vicinity of the critical point, whereas ${\ensuremath{\nu}}_{m}$ gives the minimum on the entire phase diagram.