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

The Riemann hypothesis, which states that the non-trivial 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. Inspired by the P\'olya-Hilbert conjecture, we propose a new approach to finding a physical system to study the Riemann zeros, which in contrast to previous examples, is based on applying a time-periodic driving field. This driving allows us to mould the quasienergies of the system (the analogue of the eigenenergies in the absence of driving), 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.Comment: 6 pages, accepted for publication in Phys. Rev.

Concentrations of Polychlorinated Biphenyls (PCBs), Polychlorinated Dibenzo-p-dioxins and Furans (PCDD/Fs), and Polybrominated Diphenyl Ethers (PBDEs) as Functions of Sample Depth in Killer Whale (Orcinus orca) Blubber

Concentrations of polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs), and polybrominated diphenyl ethers (PBDEs) were examined as a function of depth in killer whale (Orcinus orca) blubber samples. Lipid-normalized concentrations of PCBs, PCDD/Fs, and PBDEs did not display significant variation with depth in three distinct blubber layers (outer, central, and inner). Significantly more variation in contaminant concentrations were observed with depth on a wet weight basis for the killer whale sample. The current study indicates that non-invasive microdart biopsy sampling methods commonly used for monitoring contaminants in marine mammals yield representative details on contaminant burdens for chlorinated and brominated aromatic compounds in marine mammal blubber, regardless of the quantity and type of blubber sampled, provided that lipid normalization is performed on resulting analytical determinations

The dimer-RVB State of the Four-Leg Heisenberg Ladder: Interference among Resonances

We study the ground state of the 4-leg spin ladder using a dimer-RVB ansatz and the Lanczos method. Besides the well known resonance mechanism between valence bond configurations we find novel interference effects among nearby resonances.Comment: 4 pages, RevTex, 7 eps fig