Ramp, Plateau, and Wormholes without Averaging, and Hyper-non-perturbative Structures in Gravity
Abstract
Universal hallmarks of quantum chaos---such as the ramp and plateau in the spectral form factor---and the ramp's gravitational duals involving wormholes are widely interpreted as consequences of spectral or ensemble averaging. In this paper, following an earlier proposal of~\cite{Liu25c}, we develop an alternative approach: these phenomena arise as macroscopic smooth structures hidden within erratic microscopic data, which can be isolated through a smooth filter projection. Using the semiclassical Gutzwiller trace formula as a paradigmatic example, we illustrate how many features characteristic of random matrix models---including the ramp, the plateau, the spectral curve, and single-eigenvalue instantons---can be derived in the semiclassical limit without invoking ensemble or explicit spectral averages. We postulate the existence of a minimal Gutzwiller-like structure in the large-N limit of holographic systems and explore its consequences. Beyond deriving the ramp and the plateau, this Gutzwiller-like structure predicts universal rapid macroscopic oscillations in the density of states and the possible existence of hyper-instantons, both of which involve double exponentials in 1/N2. On the gravity side, we demonstrate how spacetime wormholes enable the construction of emergent hyper-non-perturbative objects---such as baby-universe and wormhole condensates---which yield double exponential effects in GN. This mirrors the postulated boundary Gutzwiller-like structure and provides a dual gravitational derivation of the universal rapid macroscopic oscillations in the density of states and the spectral plateau.
Related
- Mathematical Classification of Switching Types and Hierarchical Structures: Three Switching Types, Six Hierarchical Structures, Coefficient of Variation Lower Bound, and Discretization Plateau Effect in the k-Regime Linear Switching Model
- Unique equivariant pseudo expectation and generalized Powers averaging for crossed product
- end point estimates for the bilinear circular averaging operator
- Dimensionality-induced critical phase transition in stochastic Lotka-Volterra equation: From statistical averaging to systemic tipping point
- Global Integrated Null Energy Contribution : Classification of Traversable Wormholes
BibTeX
@misc{liu2026ramp,
title = {{Ramp, Plateau, and Wormholes without Averaging, and Hyper-non-perturbative Structures in Gravity}},
author = {Hong Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.02743},
eprint = {2608.02743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02743},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ramp, Plateau, and Wormholes without Averaging, and Hyper-non-perturbative Structures in Gravity
AU - Hong Liu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2608.02743
UR - https://arxiv.org/abs/2608.02743
AB - Universal hallmarks of quantum chaos---such as the ramp and plateau in the spectral form factor---and the ramp's gravitational duals involving wormholes are widely interpreted as consequences of spectral or ensemble averaging. In this paper, following an earlier proposal of~\cite{Liu25c}, we develop an alternative approach: these phenomena arise as macroscopic smooth structures hidden within erratic microscopic data, which can be isolated through a smooth filter projection. Using the semiclassical Gutzwiller trace formula as a paradigmatic example, we illustrate how many features characteristic of random matrix models---including the ramp, the plateau, the spectral curve, and single-eigenvalue instantons---can be derived in the semiclassical limit without invoking ensemble or explicit spectral averages. We postulate the existence of a minimal Gutzwiller-like structure in the large-N limit of holographic systems and explore its consequences. Beyond deriving the ramp and the plateau, this Gutzwiller-like structure predicts universal rapid macroscopic oscillations in the density of states and the possible existence of hyper-instantons, both of which involve double exponentials in 1/N^2. On the gravity side, we demonstrate how spacetime wormholes enable the construction of emergent hyper-non-perturbative objects---such as baby-universe and wormhole condensates---which yield double exponential effects in G_N. This mirrors the postulated boundary Gutzwiller-like structure and provides a dual gravitational derivation of the universal rapid macroscopic oscillations in the density of states and the spectral plateau.
ER -