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Center for Nonlinear Studies |
Quantum effects in material systems are often pronounced at low energies and become insignificant at high temperatures. As we elaborate here, this common occurrence might not, however, hold universally. We find that, perhaps counterintuitively, certain quantum effects may follow the opposite route and become progressively sharper so as to emerge in the "classical" high temperature limit. In the current work, we invoke simple elements of the WKB approximation as applied to general Hamiltonians, extend the usual kinetic theory by taking into account a possible fundamental quantum time scale, and apply ideas from transition state theory. On average, the extrapolated high temperature viscosity of general liquids may tend to a value set by the product of the particle number density n and Planck's constant h. We compare this theoretical result with experimental measurements of an ensemble of 23 metallic fluids where this seems to indeed be the case. The extrapolated high temperature viscosity of each of these liquids divided (for each respective fluid) by its value of nh veers towards a Gaussian with an ensemble average value that is close to unity up to an error of size 0.6%. We invoke similar ideas to discuss other transport properties to suggest how simple behaviors may appear including resistivity saturation and linear T resistivity may appear very naturally. Our approach suggests that minimal time lags may be present in fluid dynamics (which in the continuum follows the Navier-Stokes equation).
Host: Cristian Batista