Hilbert-P\'{o}lya conjecture via critical pseudo-magnetic degrees of freedom

TL;DR

This paper links critical pseudo-magnetic fields in layered materials to the zeros of the Riemann Xi function, proposing a quantum operator realization that offers insights into the Hilbert-Pólya conjecture.

Contribution

It introduces a novel connection between pseudo-magnetic fields, Feshbach resonances, Lee-Yang zeros, and the Riemann Xi function, providing a potential physical realization of the Hilbert-Pólya conjecture.

Findings

Identifies a correspondence between pseudo-magnetic fields and Riemann Xi zeros.

Proposes a quantum operator that could realize the Hilbert-Pólya conjecture.

Links phase transitions in layered materials to fundamental number theory concepts.

Abstract

Motivated by a recent pseudo-spin model for monolayer-bilayer phase transitions in silver-based honeycomb layered materials, we propose that the critical pseudo-magnetic fields in such systems correspond to both the infinite-channel Feshbach resonance widths of a (Fermi-Dirac/Bose-Einstein/etc.) condensate in 2 dimensions, and equivalently to the Lee-Yang zeros of the Ising model of two pseudo-spins with a partition function corresponding to a class of functions that must include the Riemann Xi function. Identifying the quantum-mechanical operator that yields the discontinuous/random/topological spectrum of the critical pseudo-magnetic fields in such systems offers a tenable realisation of the Hilbert-P\'{o}lya conjecture.