Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates

We present relativistic linear stability equations (RLSE) for quasi-relativistic cold atoms in a honeycomb optical lattice. These equations are derived from first principles and provide a method for computing stabilities of arbitrary localized solutions of the nonlinear Dirac equation (NLDE), a relativistic generalization of the nonlinear Schr\"odinger equation. We present a variety of such localized solutions: skyrmions, solitons, vortices, and half-quantum vortices, and study their stabilities via the RLSE. When applied to a uniform background, our calculations reveal an experimentally observable effect in the form of Cherenkov radiation. Remarkably, the Berry phase from the bipartite structure of the honeycomb lattice induces a boson-fermion transmutation in the quasi-particle operator statistics.Comment: 6 pages, 3 figure

Dynamin-related protein 1 is required for normal mitochondrial bioenergetic and synaptic function in CA1 hippocampal neurons.

Disrupting particular mitochondrial fission and fusion proteins leads to the death of specific neuronal populations; however, the normal functions of mitochondrial fission in neurons are poorly understood, especially in vivo, which limits the understanding of mitochondrial changes in disease. Altered activity of the central mitochondrial fission protein dynamin-related protein 1 (Drp1) may contribute to the pathophysiology of several neurologic diseases. To study Drp1 in a neuronal population affected by Alzheimer's disease (AD), stroke, and seizure disorders, we postnatally deleted Drp1 from CA1 and other forebrain neurons in mice (CamKII-Cre, Drp1lox/lox (Drp1cKO)). Although most CA1 neurons survived for more than 1 year, their synaptic transmission was impaired, and Drp1cKO mice had impaired memory. In Drp1cKO cell bodies, we observed marked mitochondrial swelling but no change in the number of mitochondria in individual synaptic terminals. Using ATP FRET sensors, we found that cultured neurons lacking Drp1 (Drp1KO) could not maintain normal levels of mitochondrial-derived ATP when energy consumption was increased by neural activity. These deficits occurred specifically at the nerve terminal, but not the cell body, and were sufficient to impair synaptic vesicle cycling. Although Drp1KO increased the distance between axonal mitochondria, mitochondrial-derived ATP still decreased similarly in Drp1KO boutons with and without mitochondria. This indicates that mitochondrial-derived ATP is rapidly dispersed in Drp1KO axons, and that the deficits in axonal bioenergetics and function are not caused by regional energy gradients. Instead, loss of Drp1 compromises the intrinsic bioenergetic function of axonal mitochondria, thus revealing a mechanism by which disrupting mitochondrial dynamics can cause dysfunction of axons

Quasienergy spectra of a charged particle in planar honeycomb lattices

The low energy spectrum of a particle in planar honeycomb lattices is conical, which leads to the unusual electronic properties of graphene. In this letter we calculate the quasienergy spectra of a charged particle in honeycomb lattices driven by a strong AC field, which is of fundamental importance for its time-dependent dynamics. We find that depending on the amplitude, direction and frequency of external field, many interesting phenomena may occur, including band collapse, renormalization of velocity of ``light'', gap opening etc.. Under suitable conditions, with increasing the magnitude of the AC field, a series of phase transitions from gapless phases to gapped phases appear alternatively. At the same time, the Dirac points may disappear or change to a line. We suggest possible realization of the system in Honeycomb optical lattices.Comment: 4+ pages, 5 figure