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

Mario J. Pinheiro

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 $A(θ)=A_0\cos(θ+δ)$ and achieves quantitative agreement ($χ^2/\mathrm{dof}=0.50$, $p=0.86$) 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.

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

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 and achieves quantitative agreement (, ) with high-precision counting experiments exhibiting 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.

Paper Structure

This paper contains 7 sections, 2 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Non-Hermitian Causal Memory Framework
  3. Why Spectral Analysis Fails
  4. Observable Signatures
  5. Experimental Validation
  6. Discussion
  7. Conclusion

Figures (3)

  • Figure 1: Similarity profile from non-Hermitian causal memory model. Parameters: $\alpha=0.8$, $\beta=0.15$, $\gamma=0.6$, $A=2.8$, $\tau_c=2h$, $\sigma=15s$, $\epsilon=0.04$. Error bands show $\pm1\sigma$ from 100 realizations. Inset: Comparison to stationary Poisson process showing absence of structure.
  • Figure 2: Asymmetric transition at causal scale $T_s$. Solid curve: ensemble average over 5 seeds. Dashed: symmetric Lorentzian for comparison. The asymmetry is a direct signature of non-Hermitian dynamics.
  • Figure 3: Validation against experimental data. Left: Model predictions (red) vs. observed counts (blue). Right: Normalized residuals showing agreement within $\pm2\sigma$ for the transition region.