Minimal quantum viscosity from fundamental physical constants.

Trachenko, K; Brazhkin, V V · Sci Adv · 2020

basic_science · Level V

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Abstract

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: <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mrow><msub><mi>ν</mi> <mi>m</mi></msub> <mo>=</mo> <mfrac><mn>1</mn> <mrow><mn>4</mn> <mi>π</mi></mrow> </mfrac> <mfrac><mi>ℏ</mi> <mrow> <msqrt> <mrow><msub><mi>m</mi> <mi>e</mi></msub> <mi>m</mi></mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> </math> , where <i>m<sub>e</sub></i> and <i>m</i> are electron and molecule masses. We subsequently introduce a new property, the "elementary" viscosity ι with the lower bound set by fundamental physical constants and notably involving the proton-to-electron mass ratio: <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mrow><msub><mi>ι</mi> <mi>m</mi></msub> <mo>=</mo> <mfrac><mi>ℏ</mi> <mrow><mn>4</mn> <mi>π</mi></mrow> </mfrac> <msup><mrow><mo>(</mo> <mfrac> <mrow><msub><mi>m</mi> <mi>p</mi></msub> </mrow> <mrow><msub><mi>m</mi> <mi>e</mi></msub> </mrow> </mfrac> <mo>)</mo></mrow> <mrow><mfrac><mn>1</mn> <mn>2</mn></mfrac> </mrow> </msup> </mrow> </mrow> </math> , where <i>m<sub>p</sub></i> 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.