Non-Hermitian Causal Memory Generates Observable Temporal Correlations Invisible to Spectral Analysis

TL;DR

This paper introduces a new class of non-Hermitian causal processes that produce temporal correlations undetectable by spectral analysis, revealing fundamental limitations of traditional spectral methods.

Contribution

The authors demonstrate that non-Hermitian causal memory kernels generate observable temporal correlations invisible to spectral analysis, with a model validated by high-precision experiments.

Findings

Temporal correlations are invisible to spectral methods.

The model predicts an asymmetric transition profile with specific orientation dependence.

Quantitative agreement with experiments shows high significance (p<10^{-15}).

Abstract

We identify a new class of non-Hermitian causal processes that produce statistically significant temporal correlations invisible to conventional spectral methods. Using a generative model with a strictly causal memory kernel, we demonstrate that time-asymmetric stochastic processes naturally yield sharp transitions at characteristic scales that appear as localized structures in similarity space but leave no trace in power spectra. The model predicts an asymmetric transition profile with orientation-dependent asymmetry parameter $A(\theta)=A_0\cos(\theta+\delta)$ and achieves quantitative agreement ($\chi^2/\mathrm{dof}=0.50$, $p=0.86$) with high-precision counting experiments exhibiting $p<10^{-15}$ significance. These results establish a fundamental limitation of spectral analysis for non-Hermitian, non-stationary processes and provide experimentally testable signatures of causal memory in open quantum systems.