  In high energy heavy-ion collisions, the two colliding nuclei pass through
each other leaving behind an almost baryon free central rapidity region. Most
of the baryons are carried away by the nuclear remnants and are located in the
so-called fragmentation regions. In previous papers
\cite{Li:2016wzh,Li:2018ini}, it has been argued that very high baryon
densities, more than ten times larger than the normal nuclear density, can be
achieved in these fragmentation regions. In this paper, we assume the high
baryon density matter is thermalized at the same time as the baryon-free
quark-gluon plasma in the central rapidity region. We perform a 1+1D (temporal
+ longitudinal) hydrodynamic simulation covering both the fragmentation regions
and the central rapidity region with the baryon diffusion equation included.
Baryons are found to diffuse from the fragmentation regions to the central
rapidity region driven by fugacity gradients. The baryon chemical potential at
freezeout monotonically increases from the central rapidity region to the
fragmentation regions, suggesting a rapidity scan in high energy heavy-ion
collisions might be helpful in searching for the critical point of the QCD
phase diagram.
