Roton (source code)
= Roton
{title2=$\epsilon(p)\simeq\Delta+(p-p_0)^2/(2m_r)$}
{wiki}
A <roton> is an excitation near a local minimum of a <superfluid>'s <dispersion relation> at nonzero <momentum> $p_0$. The displayed local approximation defines a positive <energy> gap $\Delta$ and positive curvature <effective mass> $m_r$; it is not a free helium atom or a macroscopic <quantum vortex>.<On the Theory of Superfluidity of Helium II by Lev Davidovich Landau>[Landau, On the Theory of Superfluidity of Helium II (1947), p.91, Fig.1]{ref} In the stipulated plot, these correspond to $p_0=2p_*$, $\Delta=0.6E_*$ and $m_r=p_*^2/(4E_*)$. The plot illustrates how a low <energy> at appreciable <momentum> can lower the <Landau criterion> below the <speed of sound>, without assigning any measured parameter to real <helium>.
Landau's 1947 revision joined the low-<momentum> linear part to a spectrum with a finite-<momentum> minimum, retaining the macroscopic <superfluid> theory while changing its excitation model.<On the Theory of Superfluidity of Helium II by Lev Davidovich Landau>[Landau (1947), p.91, spectrum revision]{ref}
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