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    Projected SO(5) Hamiltonian for Cuprates and Its Applications

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    The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and superconducting fluctuations of underdoped cuprates in terms of four bosons moving on a coarse grained lattice. A simple mean field approximation can explain some key feautures of the experimental phase diagram: (i) The Mott transition between antiferromagnet and superconductor, (ii) The increase of T_c and superfluid stiffness with hole concentration x and (iii) The increase of antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase. We apply this theory to explain the ``two gaps'' problem found in underdoped cuprate Superconductor-Normal- Superconductor junctions. In particular we explain the sharp subgap Andreev peaks of the differential resistance, as signatures of the antiferromagnetic resonance (the magnon mass gap). A critical test of this theory is proposed. The tunneling charge, as measured by shot noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather than by Delta Q=e as in conventional superconductors.Comment: 3 EPS figure

    Direct effects of transcranial electric stimulation on brain circuits in rats and humans

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    Transcranial electric stimulation is a non-invasive tool that can influence brain activity; however, the parameters necessary to affect local circuits in vivo remain to be explored. Here, we report that in rodents and human cadaver brains, ~75% of scalp-applied currents are attenuated by soft tissue and skull. Using intracellular and extracellular recordings in rats, we find that at least 1 mV/mm voltage gradient is necessary to affect neuronal spiking and subthreshold currents. We designed an ‘intersectional short pulse’ stimulation method to inject sufficiently high current intensities into the brain, while keeping the charge density and sensation on the scalp surface relatively low. We verify the regional specificity of this novel method in rodents; in humans, we demonstrate how it affects the amplitude of simultaneously recorded EEG alpha waves. Our combined results establish that neuronal circuits are instantaneously affected by intensity currents that are higher than those used in conventional protocols
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