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Viscosity of fluids is strongly system-dependent, varies across many orders of magnitude and depends on molecular interactions and structure in a complex way not amenable to first-principles theories. Despite the variations and theoretical difficulties, we find a new quantity setting the minimal kinematic viscosity of fluids: $ u_m=frac{1}{4pi}frac{hbar}{sqrt{m_em}}$, where $m_e$ and $m$ are electron and molecule masses. We subsequently introduce a new property, the elementary viscosity $iota$ with the lower bound set by fundamental physical constants and notably involving the proton-to-electron mass ratio: $iota_m=frac{hbar}{4pi}left({frac{m_p}{m_e}}right)^{frac{1}{2}}$, where $m_p$ is the proton mass. We discuss the connection of our result to the bound found by Kovtun, Son and Starinets in strongly-interacting field theories.
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Two dimensionless fundamental physical constants, the fine structure constant $alpha$ and the proton-to-electron mass ratio $frac{m_p}{m_e}$ are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant which provides the upper bound for the speed of sound in condensed phases, $v_u$. We find that $frac{v_u}{c}=alphaleft(frac{m_e}{2m_p}right)^{frac{1}{2}}$, where $c$ is the speed of light in vacuum. We support this result by a large set of experimental data and first principles computations for atomic hydrogen. Our result expands current understanding of how fundamental constants can impose new bounds on important physical properties.
Could it be that the matter from the electrons in high Tc superconductors is of a radically new kind that may be called many body entangled compressible quantum matter? Much of this text is intended as an easy to read tutorial, explaining recent theoretical advances that have been unfolding at the cross roads of condensed matter- and string theory, black hole physics as well as quantum information theory. These developments suggest that the physics of such matter may be governed by surprisingly simple principles. My real objective is to present an experimental strategy to test critically whether these principles are actually at work, revolving around the famous linear resistivity characterizing the strange metal phase. The theory suggests a very simple explanation of this unreasonably simple behavior that is actually directly linked to remarkable results from the study of the quark gluon plasma formed at the heavy ion colliders: the fast hydrodynamization and the minimal viscosity. This leads to high quality predictions for experiment: the momentum relaxation rate governing the resistivity relates directly to the electronic entropy, while at low temperatures the electron fluid should become unviscous to a degree that turbulent flows can develop even on the nanometre scale.
The location-scale model is usually present in physics and chemistry in connection to the Birge ratio method for the adjustment of fundamental physical constants such as the Planck constant or the Newtonian constant of gravitation, while the random effects model is the commonly used approach for meta-analysis in medicine. These two competitive models are used to increase the quoted uncertainties of the measurement results to make them consistent. The intrinsic Bayes factor (IBF) is derived for the comparison of the random effects model to the location-scale model, and we answer the question which model performs better for the determination of the Newtonian constant of gravitation. The results of the empirical illustration support the application of the Birge ratio method which is currently used in the adjustment of the CODATA 2018 value for the Newtonian constant of gravitation together with its uncertainty. The results of the simulation study illustrate that the suggested procedure for model selection is decisive even when data consist of a few measurement results.
We discuss quantum analogues of minimal surfaces in Euclidean spaces and tori.
We estimate the cosmological variation of the proton-to-electron mass ratio mu=m_p/m_e by measuring the wavelengths of molecular hydrogen transitions in the early universe. The analysis is performed using high spectral resolution observations (FWHM ~ 7 km/s) of two damped Lyman-alpha systems at z_{abs}=2.3377 and 3.0249 observed along the lines of sight to the quasars Q 1232+082 and Q 0347-382 respectively. The most conservative result of the analysis is a possible variation of mu over the last ~ 10 Gyrs, with an amplitude Deltamu/mu = (5.7+-3.8)x10^{-5}. The result is significant at the 1.5sigma level only and should be confirmed by further observations. This is the most stringent estimate of a possible cosmological variation of mu obtained up to now.
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