Title: Statics and dynamics of a self-bound dipolar matter-wave droplet,
Abstract: We study the statics and dynamics of a stable, mobile, self-bound
three-dimensional dipolar matter-wave droplet created in the presence of a tiny
repulsive three-body interaction. In frontal collision with an impact parameter
and in angular collision at large velocities {along all directions} two
droplets behave like quantum solitons. Such collision is found to be quasi
elastic and the droplets emerge undeformed after collision without any change
of velocity. However, in a collision at small velocities the axisymmeric
dipolar interaction plays a significant role and the collision dynamics is
sensitive to the direction of motion. For an encounter along the $z$ direction
at small velocities, two droplets, polarized along the $z$ direction, coalesce
to form a larger droplet $-$ a droplet molecule. For an encounter along the $x$
direction at small velocities, the same droplets stay apart and never meet each
other due to the dipolar repulsion. The present study is based on an analytic
variational approximation and a numerical solution of the mean-field
Gross-Pitaevskii equation using the parameters of $^{52}$Cr atoms.