  As shown by broad-band observations, pulsar wind nebulae (PWNe) are
characterized by a broken power-law spectrum of synchrotron emission. Based on
the modern magnetohydrodynamic (MHD) turbulence theories, we investigate the
re-acceleration of electrons in the PWN through the adiabatic stochastic
acceleration (ASA), which arises from fundamental dynamics of MHD turbulence.
The ASA acts to flatten the injected energy spectrum of electrons at low
energies, while synchrotron cooling results in a steep spectrum of electrons at
high energies. Their dominance in different energy ranges leads to a flat radio
spectrum ($F_\nu$) and a steep X-ray spectrum. Our analytical spectral shapes
generally agree well with the observed synchrotron spectra of radio- and
X-ray-bright PWNe. The spectral break corresponding to the balance between the
ASA and synchrotron losses provides a constraint on the acceleration timescale
of the ASA and the magnetic field strength in the PWN.
