Effects of density-dependent quark mass on phase diagram of three-flavor quark matter

Considering the density dependence of quark mass, we investigate the phase transition between the (unpaired) strange quark matter and the color-flavor-locked matter, which are supposed to be two candidates for the ground state of strongly interacting matter. We find that if the current mass of strange quark $m_s$ is small, the strange quark matter remains stable unless the baryon density is very high. If $m_s$ is large, the phase transition from the strange quark matter to the color-flavor-locked matter in particular to its gapless phase is found to be different from the results predicted by previous works. A complicated phase diagram of three-flavor quark matter is presented, in which the color-flavor-locked phase region is suppressed for moderate densities.Comment: 4 figure

Instability of the solitary waves for the generalized Boussinesq equations

In this work, we consider the following generalized Boussinesq equation \begin{align*} \partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad (t,x)\in\mathbb R\times \mathbb R, \end{align*} with $0<p<\infty$. This equation has the traveling wave solutions $\phi_\omega(x-\omega t)$, with the frequency $\omega\in (-1,1)$ and $\phi_\omega$ satisfying \begin{align*} -\partial_{xx}{\phi}_{\omega}+(1-{\omega^2}){\phi}_{\omega}-{\phi}_{\omega}^{p+1}=0. \end{align*} Bona and Sachs (1988) proved that the traveling wave $\phi_\omega(x-\omega t)$ is orbitally stable when $0<p<4,$ $\frac p4<\omega^2<1$. Liu (1993) proved the orbital instability under the conditions $0<p<4,$ $\omega^2<\frac p4$ or $p\ge 4,$ $\omega^2<1$. In this paper, we prove the orbital instability in the degenerate case $0<p<4,\omega^2=\frac p4$ .Comment: 29 page