Finding zeros of the Riemann zeta function by periodic driving of cold atoms

Abstract

The Riemann hypothesis, which states that the nontrivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. We propose here an approach to finding a physical system to study the Riemann zeros, which is based on applying a time-periodic driving field. This driving allows us to tune the quasienergies of the system (the analog of the eigenenergies for static systems), so that they are directly governed by the zeta function. We further show by numerical simulations that this allows the Riemann zeros to be measured in currently accessible cold- atom experiments.