  Considering the parity symmetry related to the Dirac equation, the interplay
between energy localization and the temporal evolution of parity-defined
quantum superpositions is investigated for fermions in a magnetic field. The
unitary evolution of Dirac cat states is obtained by initializing either even
or odd principal quantum numbers in the equivalent harmonic oscillator basis in
relativistic Landau levels. Quantum operators feature well-defined selection
rules for states thus identified, exhibiting a permanent revival structure. Our
analysis is specialized for the survival probability function and for the
expectation values of spinor matrix operators, which are identified as
quantifiers of spin-parity correlations encoded in Dirac bispinors. In such a
context, the time evolving quantum state also imprints a signature on the
energy expansion. Namely, frequencies associated with revivals are doubled for
each revival order, being observed up to a so-called super revival time scale.
Results show that Dirac cat states exhibit a fractional revival structure,
which works as a probe of suppressions and regenerations of intrinsic
correlations driven by the discrete spin-parity degrees of freedom of Dirac
bispinors.
