Physical realization and origins of the Riemann Hypothesis

Determine a genuine physical realization of the Riemann Hypothesis by identifying deeper connections and the physical origins of the hypothesis within experimentally realizable quantum systems.

Background

The authors survey prior attempts to connect the Riemann zeta function with physical systems and highlight that, despite progress via engineered spectra and tailored states, a genuine physical realization and clear explanation of the RH’s physical origins have not been established. Their work proposes a direct correspondence between dynamical quantum phase transitions and the nontrivial zeros, offering an experimentally accessible route to probe these questions.

This open direction seeks not only a mapping but a fundamental understanding of how physical principles could underlie the RH, potentially revealing why the zeros should obey the critical-line structure and how such behavior emerges from quantum dynamics.

References

The search for a genuine physical realization, deeper connections and possible origins of the RH remains unknown.

— The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions  (2511.11199 - Wei et al., 14 Nov 2025) in Introduction

Whether the low-frequency residual is the inverse-spectral image of finite-height arithmetic corrections associated with primes and prime powers remains an open question.

— Hidden Dyson Universality in Inverse-Spectral Geometry  (2608.13475 - Hayashi et al., 13 Aug 2026) in Section “Shell-resolved geometry”