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.
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BibTeX
@misc{abellan2026transient,
title = {{Transient Coherence and Multiscale Spectral Structure after a Mass Quench in a 1+1-Dimensional Scalar Field}},
author = {Gabriel Abellán and Nelson Bolívar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31884},
eprint = {2609.31884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31884},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transient Coherence and Multiscale Spectral Structure after a Mass Quench in a 1+1-Dimensional Scalar Field
AU - Gabriel Abellán
AU - Nelson Bolívar
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31884
UR - https://arxiv.org/abs/2609.31884
AB - 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.
ER -