Hydrodynamic limit of order book dynamics

In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a certain sense. We also test our fluid approximation on data. The empirical results suggest that the approximation is reasonably good for liquidly--traded stocks in certain time periods

Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots

Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage

A simple scheme is presented to generate n-qubit W state with rf-superconducting quantum interference devices (rf-SQUIDs) in cavity QED through adiabatic passage. Because of the achievable strong coupling for rf-SQUID qubits embedded in cavity QED, we can get the desired state with high success probability. Furthermore, the scheme is insensitive to position inaccuracy of the rf-SQUIDs. The numerical simulation shows that, by using present experimental techniques, we can achieve our scheme with very high success probability, and the fidelity could be eventually unity with the help of dissipation.Comment: to appear in Phys. Rev.

Surface reconstruction, premelting, and collapse of open-cell nanoporous Cu via thermal annealing

We systematic investigate the collapse of a set of open-cell nanoporous Cu (np-Cu) with the same porosity and shapes, but different specific surface area, during thermal annealing, via performing large-scale molecular dynamics simulations. Surface premelting is dominated in their collapses, and surface premelting temperatures reduce linearly with the increase of specific surface area. The collapse mechanisms are different for np-Cu with different specific surface area. If the specific surface area less than a critical value ($\sim$ 2.38 nm$^{-1}$), direct surface premelting, giving rise to the transition of ligaments from solid to liquid states, is the cause to facilitate falling-down of np-Cu during thermal annealing. While surface premelting and following recrystallization, accelerating the sloughing of ligaments and annihilation of pores, is the other mechanism, as exceeding the critical specific surface area. The recrystallization occurs at the temperatures below supercooling, where liquid is instable and instantaneous. Thermal-induced surface reconstruction prompts surface premelting via facilitating local "disordering" and "chaotic" at the surface, which are the preferred sites for surface premelting

Effective g-factor in Majorana Wires

We use the effective g-factor of subgap states, g*, in hybrid InAs nanowires with an epitaxial Al shell to investigate how the superconducting density of states is distributed between the semiconductor core and the metallic shell. We find a step-like reduction of g* and improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and g* exceeding the g-factor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zero-bias conductance peak