  Over three thousand pulsars have been discovered, but none have been
confirmed to be younger than a few hundred years. Observing a pulsar after a
supernova explosion will help us understand the properties of newborn ones,
including their capability to produce gamma-ray bursts and fast radio bursts.
Here, the possible youngest pulsar wind nebula (PWN) at the center of the SN
1986J remnant is studied. We demonstrate that the 5 GHz flux of 'PWN 1986J',
increasing with time, is consistent with a stochastic acceleration model of
PWNe developed to explain the flat radio spectrum of the Crab Nebula. We obtain
an acceleration time-scale of electrons/positrons and a decay time-scale of the
turbulence responsible for the stochastic acceleration as about 10 and 70
years, respectively. Our findings suggest that efficient stochastic
acceleration and rising radio/submm light curves are characteristic signatures
of the youngest PWNe. Follow-up ${\it ALMA}$ observations of decades-old
supernovae within a few tens of Mpc, including SN 1986J, are encouraged to
reveal the origin of the flat radio spectrum of PWNe.
