The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry-Keating hamiltonian H=(xp+px)/2 projected onto the subspace of oscillator eigenfunctions of lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert-Polya conjecture. The p-adic case is also discussed.Comment: 9 pages, no figures; v2 included more mathematical background, v3 has minor edits for clarit

Temperature dependent dynamic and static magnetic response in magnetic tunnel junctions with Permalloy layers

Ferromagnetic resonance and static magnetic properties of CoFe/Al2O3/CoFe/Py and CoFe/Al2O3/CoFeB/Py magnetic tunnel junctions and of 25nm thick single-layer Permalloy(Py) films have been studied as a function of temperature down to 2K. The temperature dependence of the ferromagnetic resonance excited in the Py layers in magnetic tunnel junctions shows knee-like enhancement of the resonance frequency accompanied by an anomaly in the magnetization near 60K. We attribute the anomalous static and dynamic magnetic response at low temperatures to interface stress induced magnetic reorientation transition at the Py interface which could be influenced by dipolar soft-hard layer coupling through the Al2O3 barrier

Enhanced spin accumulation at room temperature in graphene spin valves with amorphous carbon interfacial layers

We demonstrate a large enhancement of the spin accumulation in monolayer graphene following electron-beam induced deposition of an amorphous carbon layer at the ferromagnet-graphene interface. The enhancement is 10^4-fold when graphene is deposited onto poly(methyl metacrylate) (PMMA) and exposed with sufficient electron-beam dose to cross-link the PMMA, and 10^3-fold when graphene is deposited directly onto SiO2 and exposed with identical dose. We attribute the difference to a more efficient carbon deposition in the former case due to an increase in the presence of compounds containing carbon, which are released by the PMMA. The amorphous carbon interface can sustain very large current densities without degrading, which leads to very large spin accumulations exceeding 500 microeVs at room temperature

Noninvasive deep brain stimulation using focused energy sources

A non-invasive methodological possibility for brain stimulation through the simultaneous use of an external energy beam and an existing brain imaging system such as functional magnetic resonance imaging (fMRI) is herein proposed; the main advantage is to confine the stimulation into a single brain area, avoiding unintentional stimulation of adjoining brain regions, thus, allowing for deep brain stimulation. The methodological possibility is to be used for research, treatment and diagnosis of neurological, cognitive and neurophysiologic disorders. The method includes the simultaneous steps of applying focused thermal energy stimulation within a living brain, and monitoring such stimulation using MRI thermometry images; in addition, it includes the detection of stimulated neuronal impulses by its potentially effects in the blood oxygenation level (BOLD) fMRI response signal