Motivated by a recent experiment on a superconducting quantum
information processor, I will discuss the Floquet quantum Ising model in
the presence of integrability- and symmetry-breaking random fields. The
talk will focus on the relation between boundary spin correlations,
spectral pairings, and effects of the random fields. If time permits, I
will also touch upon self-similarity in the dynamic phase diagram of
Fibonacci-driven quantum Ising models.
 

I will present joint work with Alessandro Fazzari in which we prove precise conditional estimates for the third (non-absolute) moment of the logarithm of the Riemann zeta function, beyond the Selberg central limit theorem, both for the real and imaginary part. These estimates match predictions made in work of Keating and Snaith. We require the Riemann Hypothesis, a conjecture for the triple correlation of Riemann zeros and another ``twisted'' pair correlation conjecture which captures the interaction of a prime power with Montgomery's pair correlation function. This conjecture can be proved on a certain subrange unconditionally, and on a larger range under the assumption of a variant of the Hardy-Littlewood conjecture with good uniformity.