A Fractional Lie Group Method For Anomalous Diffusion Equations

Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion equation is used as an example to illustrate the effectiveness of the Lie group method.Comment: 5 pages,in pres

Variational Iteration Method for q

Recently, Liu extended He's variational iteration method to strongly nonlinear q-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness

Enhancing quantum entropy in vacuum-based quantum random number generator

Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator. At the same time, it directly determine the extraction ratio of true randomness from the raw data, in other words, it affects quantum random numbers generating rate obviously. In this work, considering the effects of classical noise, the best way to enhance quantum entropy in the vacuum-based quantum random number generator is explored in the optimum dynamical analog-digital converter (ADC) range scenario. The influence of classical noise excursion, which may be intrinsic to a system or deliberately induced by an eavesdropper, on the quantum entropy is derived. We propose enhancing local oscillator intensity rather than electrical gain for noise-independent amplification of quadrature fluctuation of vacuum state. Abundant quantum entropy is extractable from the raw data even when classical noise excursion is large. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the local oscillator power when classical noise excursions of the raw data is obvious.Comment: 12 pages,8 figure

A New Two-Dimensional Functional Material with Desirable Bandgap and Ultrahigh Carrier Mobility

Two-dimensional (2D) semiconductors with direct and modest bandgap and ultrahigh carrier mobility are highly desired functional materials for nanoelectronic applications. Herein, we predict that monolayer CaP3 is a new 2D functional material that possesses not only a direct bandgap of 1.15 eV (based on HSE06 computation), and also a very high electron mobility up to 19930 cm2 V-1 s-1, comparable to that of monolayer phosphorene. More remarkably, contrary to the bilayer phosphorene which possesses dramatically reduced carrier mobility compared to its monolayer counterpart, CaP3 bilayer possesses even higher electron mobility (22380 cm2 V-1 s-1) than its monolayer counterpart. The bandgap of 2D CaP3 can be tuned over a wide range from 1.15 to 0.37 eV (HSE06 values) through controlling the number of stacked CaP3 layers. Besides novel electronic properties, 2D CaP3 also exhibits optical absorption over the entire visible-light range. The combined novel electronic, charge mobility, and optical properties render 2D CaP3 an exciting functional material for future nanoelectronic and optoelectronic applications

Lie group classifications and exact solutions for time-fractional Burgers equation

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.Comment: 9 pp, accepte