Transient Coherence and Multiscale Spectral Structure after a Mass Quench in a 1+1-Dimensional Scalar Field

Abstract

A mass quench generates anomalous pair correlations that are absent from the final particle occupations. For a free real scalar field in $1+1$ dimensions, we define a bilocal observable by smearing the statistical Keldysh correlator with a Morlet kernel on the finite post-quench relative-time interval. Its excess over the dephased correlator gives a dimensionless relative coherence weight. At fixed momentum, this weight is exactly independent of the initial temperature for Gaussian thermal states evolved with the same free Hamiltonian: the common thermal amplitude cancels between numerator and denominator. The cancellation is not a purity criterion and is not exclusive to wavelets. We derive the finite-window response and show that the anomalous signal depends essentially on the observation window; an admissible zero-mean wavelet annihilates the relative-time-constant anomalous term on the full line. We compare this response with the signed finite-time Wigner spectrum and derive a distinct Gaussian-extension positivity bound. Exact smooth-quench occupations provide an independent dynamical reference. Finally, we formulate a renormalized Hartree extension and delimit the oscillatory and nonoscillatory regimes of a scalar mode on a fixed two-dimensional de Sitter background.