Stochastic Schr\"odinger Equation for a Non-Markovian Dissipative Qubit-Qutrit System

We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schr\"{o}dinger equation to generate diffusive quantum trajectories. We have established an exact quantum state diffusion (QSD) equation for the dissipative qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an important application, the non-Markovian QSD equation is employed to simulate the entanglement decay and generation measured by negativity. Finally, some steady state properties of the hybrid system are also discussed.Comment: EPL in pres

On the Theory of Spatial and Temporal Locality

This paper studies the theory of caching and temporal and spatial locality. We show the following results: (1) hashing can be used to guarantee that caches with limited associativity behave as well as fully associative cache; (2) temporal locality cannot be characterized using one, or few parameters; (3) temporal locality and spatial locality cannot be studied separately; and (4) unlike temporal locality, spatial locality cannot be managed efficiently online

Kriging Interpolating Cosmic Velocity Field

[abridged] Volume-weighted statistics of large scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of uncertainties of galaxy density bias entangled in mass-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number $n_k$ of the nearby particles to interpolate and the density $n_P$ of the observed sample are investigated. First, we find that Kriging induces $1\%$ and $3\%$ systematics at $k\sim 0.1h{\rm Mpc}^{-1}$ when $n_P\sim 6\times 10^{-2} ({\rm Mpc}/h)^{-3}$ and $n_P\sim 6\times 10^{-3} ({\rm Mpc}/h)^{-3}$, respectively. The deviation increases for decreasing $n_P$ and increasing $k$. When $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$, a smoothing effect dominates small scales, causing significant underestimation of the velocity power spectrum. Second, increasing $n_k$ helps to recover small scale power. However, for $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$ cases, the recovery is limited. Finally, Kriging is more sensitive to the variogram prior for lower sample density. The most straightforward application of Kriging on the cosmic velocity field does not show obvious advantages over the nearest-particle method (Zheng et al. 2013) and could not be directly applied to cosmology so far. However, whether potential improvements may be achieved by more delicate versions of Kriging is worth further investigation.Comment: 11 pages, 5 figures, published in PR