1+1维标量场质量淬火后的瞬态相干性与多尺度谱结构
Transient Coherence and Multiscale Spectral Structure after a Mass Quench in a 1+1-Dimensional Scalar Field
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中文总结 AI 辅助
本文研究1+1维自由实标量场质量淬火后的瞬态相干性，通过Morlet核平滑关联子定义相对相干权重，发现其独立于初始温度，并推导了窗口依赖的异常信号及重整化Hartree扩展。
中文摘要 AI 辅助
质量淬火会产生最终粒子占据数中不存在的异常对关联。对于1+1维自由实标量场，我们通过在有限淬火后相对时间间隔上用Morlet核平滑统计Keldysh关联子，定义了一个双局域可观测量。其相对于去相位关联子的超出量给出了无量纲的相对相干权重。在固定动量下，对于由同一自由哈密顿量演化的高斯热态，该权重精确地独立于初始温度：公共热振幅在分子和分母之间抵消。这种抵消不是纯度判据，也并非小波所独有。我们推导了有限窗口响应，并表明异常信号本质上依赖于观测窗口；一个容许的零均值小波在全线上湮灭相对时间常数异常项。我们将此响应与带符号的有限时间Wigner谱进行比较，并推导出一个不同的高斯扩展正性界。精确的平滑淬火占据数提供了独立的动力学参考。最后，我们构建了一个重整化的Hartree扩展，并界定了固定二维de Sitter背景上标量模式的振荡和非振荡区域。
英文摘要
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.
发表机构
- Universidad Central de Venezuela（委内瑞拉中央大学）
- Astrum Drive Technologies
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