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I am reading the book "The man they wouldn't let die" by Alexander Dorozynski, which is an biography of Russian theoretical physicist Lev Landau, and I have encountered this passage

Absolute zero is considered as the lowest possible temperature for any element: $-273.16^{\circ}$ C. It was long assumed that at absolute zero all molecular motion would cease; Landau was one of the first to prove this assumption incorrect.

What proof is the writer talking about here? Does anyone know about the (corresponding) original paper?

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It's nothing else than Landau's 1941 two-fluid model of superfluids (similar to helium-4) that won him the 1962 Nobel prize in physics.

Landau, L. D., The Theory of Superfluidity of Helium II, J. Phys. 5, 71 (1941)

At temperatures near absolute zero, the fluids are composed of two components, the normal fluid we know from room temperatures (and whose share goes to zero at absolute zero) and the Bose-Einstein condensate. The latter has sound waves etc. that don't stop at $T=0$. On the contrary, they like to move indefinitely because the "friction" etc. of the Bose-Einstein condensate component vanishes.

Concerning the full English version of the papers, I can only find the one-page "second part" 1947 followup now:

http://www.ufn.ru/dates/pdf/j_phys_ussr/j_phys_ussr_1947_11_1/12_landau_j_phys_ussr_1947_11_1_91.pdf

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