  In quantum Hall edge states and in other one-dimensional interacting systems,
charge fractionalization can occur due to the fact that an injected charge
pulse decomposes into eigenmodes propagating at different velocities. If the
original charge pulse has some spatial width due to injection with a given
source-drain voltage, a finite time is needed until the separation between the
fractionalized pulses is larger than their width. In the formalism of
non-equilibrium bosonization, the above physics is reflected in the separation
of initially overlapping square pulses in the effective scattering phase. When
expressing the single particle Green's function as a functional determinant of
counting operators containing the scattering phase, the time evolution of
charge fractionalization is mathematically described by functional determinants
with overlapping pulses. We develop a framework for the evaluation of such
determinants, describe the system's equilibration dynamics, and compare our
theoretical results with recent experimental findings.
