  Context. More than 10000 Jupiter Trojans have been detected so far. They are
moving around the L4 and L5 triangular Lagrangian points of the Sun-Jupiter
system and their distributions can provide important clues to the early
evolution of the Solar System.
  Aims. The number asymmetry of the L4 and L5 Jupiter Trojans is a longstanding
problem. We aim to test a new mechanism in order to explain this anomalous
feature by invoking the jumping-Jupiter scenario.
  Methods. First, we introduce the orbital evolution of Jupiter caused by the
giant planet instability in the early Solar System. In this scenario, Jupiter
could undergo an outward migration at a very high speed. We then investigate
how such a jump changes the numbers of the L4 (N4) and L5 (N5) Trojans.
  Results. The outward migration of Jupiter can distort the co-orbital orbits
near the Lagrangian points, resulting in L4 Trojans being more stable than the
L5 ones. We find that, this mechanism could potentially explain the unbiased
number asymmetry of N4/N5~1.6 for the known Jupiter Trojans. The uncertainties
of the system parameters, e.g. Jupiter's eccentricity and inclination, the
inclination distribution of Jupiter Trojans, are also taken into account and
our results about the L4/L5 asymmetry have been further validated. However, the
resonant amplitudes of the simulated Trojans are excited to higher values
compared to the current population. A possible solution is that collisions
among the Trojans may reduce their resonant amplitudes.
