Title: Quantum Quench dynamics in Non-local Luttinger Model: Rigorous Results,
Abstract: We investigate, in the Luttinger model with fixed box potential, the time
evolution of an inhomogeneous state prepared as a localized fermion added to
the noninteracting ground state. We proved that, if the state is evolved with
the interacting Hamiltonian, the averaged density has two peaks moving in
opposite directions, with a constant but renormalized velocity. We also proved
that a dynamical `Landau quasi-particle weight' appears in the oscillating part
of the averaged density, asymptotically vanishing with large time. The results
are proved with the Mattis-Lieb diagonalization method. A simpler proof with
the exact Bosonization formulas is also provided.