Time-dependent approach to many-particle tunneling in one-dimension

Employing the time-dependent approach, we investigate a quantum tunneling decay of many-particle systems. We apply it to a one-dimensional three-body problem with a heavy core nucleus and two valence protons. We calculate the decay width for two-proton emission from the survival probability, which well obeys the exponential decay-law after a sufficient time. The effect of the correlation between the two emitted protons is also studied by observing the time evolution of the two-particle density distribution. It is shown that the pairing correlation significantly enhances the probability for the simultaneous diproton decay.Comment: 9 pages, 10 eps figure

Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames

It has been proposed that mixing induced by convective overshoot can disrupt the inward propagation of carbon deflagrations in super-asymptotic giant branch stars. To test this theory, we study an idealized model of convectively bounded carbon flames with 3D hydrodynamic simulations of the Boussinesq equations using the pseudospectral code Dedalus. Because the flame propagation timescale is much longer than the convection timescale, we approximate the flame as fixed in space, and only consider its effects on the buoyancy of the fluid. By evolving a passive scalar field, we derive a {\it turbulent} chemical diffusivity produced by the convection as a function of height, $D_{\rm t}(z)$. Convection can stall a flame if the chemical mixing timescale, set by the turbulent chemical diffusivity, $D_{\rm t}$, is shorter than the flame propagation timescale, set by the thermal diffusivity, $\kappa$, i.e., when $D_{\rm t}>\kappa$. However, we find $D_{\rm t}<\kappa$ for most of the flame because convective plumes are not dense enough to penetrate into the flame. Extrapolating to realistic stellar conditions, this implies that convective mixing cannot stall a carbon flame and that "hybrid carbon-oxygen-neon" white dwarfs are not a typical product of stellar evolution.Comment: Accepted to Ap

Ordering of timescales predicts applicability of quasi-linear theory in unstable flows

We discuss the applicability of quasilinear-type approximations for a turbulent system with a large range of spatial and temporal scales. We consider a paradigm fluid system of rotating convection with a vertical and horizontal temperature gradients. In particular, the interaction of rotating with the horizontal temperature gradient drives a ``thermal wind'' shear flow whose strength is controlled by a horizontal temperature gradient. Varying the parameters systematically alters the ordering of the shearing timescale, the convective timescale, and the correlation timescale. We demonstrate that quasilinear-type approximations work well when the shearing timescale or the correlation timescale is sufficiently short. In all cases, the Generalised Quasilinear approximation (GQL) systematically outperforms the Quasilinear approximation (QL). We discuss the consequences for statistical theories of turbulence interacting with mean gradients. We conclude with comments about the general applicability of these ideas across a wide variety of non-linear physical systems.Comment: 5 pages, 3 figure