Axisymmetric Magnetorotational Instability in Viscous Accretion Disks

Axisymmetric magnetorotational instability (MRI) in viscous accretion disks is investigated by linear analysis and two-dimensional nonlinear simulations. The linear growth of the viscous MRI is characterized by the Reynolds number defined as $R_{\rm MRI} \equiv v_A^2/\nu\Omega$, where $v_A$ is the Alfv{\'e}n velocity, $\nu$ is the kinematic viscosity, and $\Omega$ is the angular velocity of the disk. Although the linear growth rate is suppressed considerably as the Reynolds number decreases, the nonlinear behavior is found to be almost independent of $R_{\rm MRI}$. At the nonlinear evolutionary stage, a two-channel flow continues growing and the Maxwell stress increases until the end of calculations even though the Reynolds number is much smaller than unity. A large portion of the injected energy to the system is converted to the magnetic energy. The gain rate of the thermal energy, on the other hand, is found to be much larger than the viscous heating rate. Nonlinear behavior of the MRI in the viscous regime and its difference from that in the highly resistive regime can be explained schematically by using the characteristics of the linear dispersion relation. Applying our results to the case with both the viscosity and resistivity, it is anticipated that the critical value of the Lundquist number $S_{\rm MRI} \equiv v_A^2/\eta\Omega$ for active turbulence depends on the magnetic Prandtl number $S_{{\rm MRI},c} \propto Pm^{1/2}$ in the regime of $Pm \gg 1$ and remains constant when $Pm \ll 1$, where $Pm \equiv S_{\rm MRI}/R_{\rm MRI} = \nu/\eta$ and $\eta$ is the magnetic diffusivity.Comment: Accepted for publication in ApJ -- 18 pages, 9 figures, 1 tabl

Local Simulations of the Magneto-rotational Instability in Core-Collapse Supernovae

Bearing in mind the application to core-collapse supernovae, we study nonlinear properties of the magneto-rotational instability (MRI) by means of three- dimensional simulations in the framework of a local shearing box approximation. By changing systematically the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear- vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress ($>$) and the shear- vorticity ratio ($g_q$) as $> \propto g_q^{\delta}$ with its index $\delta \sim 0.5$. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has slightly smaller power-law index ($\sim 0.36$). By modeling the effect of viscous heating rates due to the MRI turbulence, we show that the stronger magnetic fields or the larger shear rates initially imposed lead to the higher dissipation rates. For a rapidly rotating PNS with the spin period in milliseconds and with strong magnetic fields of $10^{15}$ G, the energy dissipation rate is estimated to exceed $10^{51} {\rm erg\ sec^{-1}}$. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by the MRI-driven turbulence, which we speculate, on one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface, on the other hand the energy deposition there might be potentially favorable for the working of the neutrino-heating mechanism.Comment: 12 pages, 8 figures, Accepted for publication in Ap

Continuous variable entanglement on a chip

Encoding quantum information in continuous variables (CV)---as the quadrature of electromagnetic fields---is a powerful approach to quantum information science and technology. CV entanglement---light beams in Einstein-Podolsky-Rosen (EPR) states---is a key resource for quantum information protocols; and enables hybridisation between CV and single photon discrete variable (DV) qubit systems. However, CV systems are currently limited by their implementation in free-space optical networks: increased complexity, low loss, high-precision alignment and stability, as well as hybridisation, demand an alternative approach. Here we show an integrated photonic implementation of the key capabilities for CV quantum technologies---generation and characterisation of EPR beams in a photonic chip. Combined with integrated squeezing and non-Gaussian operation, these results open the way to universal quantum information processing with light

Compressible streaming instabilities in rotating thermal viscous objects

We study electromagnetic streaming instabilities in thermal viscous regions of rotating astrophysical objects, such as, protostellar and protoplanetary magnetized accretion disks, molecular clouds, their cores, and elephant trunks. The obtained results can also be applied to any regions of interstellar medium, where different equilibrium velocities between charged species can arise. We consider a weakly and highly ionized three-component plasma consisting of neutrals and magnetized electrons and ions. The vertical perturbations along the background magnetic field are investigated. The effect of perturbation of collisional frequencies due to density perturbations of species is taken into account. The growth rates of perturbations are found in a wide region of wave number spectrum for media, where the thermal pressure is larger than the magnetic pressure. It is shown that in cases of strong collisional coupling of neutrals with ions the contribution of the viscosity is negligible.Comment: Accepted for publication in "Astrophysical Journal