Observation of Universal Spectral Moments and the Dynamic Dispersive-to-Proliferative Transition

TL;DR

This paper demonstrates that spectral moments serve as boundary-robust bulk observables in finite non-Hermitian lattices, revealing a dispersive-to-proliferative transition driven by bulk properties rather than spectral boundary sensitivity.

Contribution

It introduces a unified acoustic platform for spectral reconstruction, develops a loop-counting theory for finite-size effects, and uncovers a bulk transition independent of spectral boundary sensitivity.

Findings

Spectral moments remain nearly invariant across different boundary geometries.

Finite-size deviations are quantitatively captured by a loop-counting theory.

A bulk dispersive-to-proliferative transition is observed, independent of spectral boundary effects.

Abstract

In non-Hermitian systems, spectra can be maximally boundary-sensitive, yet bulk physics need not be. Here we experimentally show that spectral moments provide boundary-robust bulk observables in finite non-Hermitian lattices, even when the spectra undergo dramatic geometry-dependent reshaping due to the skin effect. Using a unified acoustic platform with full spectral reconstruction and time-domain access, we probe one-, two- and three-dimensional lattices and demonstrate that spectral moments remain nearly invariant across distinct boundary geometries while the corresponding complex spectra differ strongly. To connect the thermodynamic theorem to realistic finite systems, we develop a loop-counting theory that identifies the physical origin of finite-size deviations in terms of missing boundary loops, quantitatively captures the corrections, and predicts a scaling law, which we verify experimentally. Beyond acoustic spectroscopy, we reveal a counterintuitive dynamical consequence of moment invariance: a dispersive-to-proliferative bulk transition governed by bulk moment structure rather than spectral boundary sensitivity. As a result, local bulk dynamics can remain stable (dispersive) even in a $\mathcal{PT}$-broken spectral regime, challenging the conventional expectation that $\mathcal{PT}$ breaking necessarily implies feedback-induced dynamical instability (proliferation) through exponentially amplifying spectral components. These results establish spectral moments as practical bulk descriptors for finite non-Hermitian matter and open a route to extracting and controlling intrinsic bulk behavior in realistic wave-based non-Hermitian devices.