Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

We calculate numerically the entanglement entropy of free fermion ground states in one-, two- and three-dimensional Anderson models, and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.Comment: 4 pages, 4 figures, 3 references adde

A Perspective on Organic Agriculture in China - Opportunities and Challenges

With the rapid development of international production and trade in organic food, organic agriculture is also boosting in China. The milestone of Chinese organic agri-culture was set in 1990 with the first export of a certified organic product (tea) from Lin’an county of Zhejiang Province, China, which marked the launch of organic pro-duction in China. By the end of 2005, there had been about 4.384 million ha organic land, including 1.694 million ha organic, 0.61 million ha conversion as well as 2.08 million ha collection area, about half of which is certified area. About 4.93 million tons organic products and nearly 1600 projects had been certified with 300~400 varieties. According to the above data, now China ranks the 3rd largest country of organic production in the world. In China, organic development mostly is export oriented, the export products include beans, rice, tea, mushroom, vegetable, processed oil and herbs, etc. According to the certifying body COFCC of Ministry of Agriculture (MOA), the value of exported organic products increased from 0.3 million USD in 1995 to 0.35 billion USD at the end of the year 2004. Chinese domestic organic market started from 2000. Presently, most of the products sold in domestic markets are certified by COFCC and OFDC in some largest cities such as Beijing, Shanghai, Guangzhou, Nanjing and Shenzhen, etc. The price of the organic products is often up to 3 times the price of conventional products. Average organic food consumption accounts for 0.08% of the conventional food (LI 2006)

THz detection and amplification using plasmonic Field Effect Transistors driven by DC drain currents

We report on the numerical and theoretical results of sub-THz and THz detection by a current-driven InGaAs/GaAs plasmonic Field-Effect Transistor (TeraFET). New equations are developed to account for the channel length dependence of the drain voltage and saturation current. Numerical simulation results demonstrate that the effect of drain bias current on the source-to-drain response voltage (dU) varies with the device channel length. In a long-channel TeraFET where plasmonic oscillations cannot reach the drain, dU is always positive and rises rapidly with increasing drain current. For a short device in which plasmonic oscillations reach the drain, the current-induced nonuniform electric field leads to a negative response, agreeing with previous observations. At negative dU, the amplitude of the small-signal voltage at the drain side becomes larger than that at the source side. Thus, the device effectively serves as a THz amplifier in this condition. Under the resonant mode, the negative response can be further amplified near the resonant peaks. A new expression of dU is proposed to account for this resonant effect. Based on those expressions, a current-driven TeraFET spectrometer is proposed. The ease of implementation and simplified calibration procedures make it competitive or superior compared with other TeraFET-based spectrometers.Comment: 23 pages, 11 figures, 1 tabl

EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty

Autoregressive decoding makes the inference of Large Language Models (LLMs) time-consuming. In this paper, we reconsider speculative sampling and derive two key observations. Firstly, autoregression at the feature (second-to-top-layer) level is more straightforward than at the token level. Secondly, the inherent uncertainty in feature (second-to-top-layer) level autoregression constrains its performance. Based on these insights, we introduce EAGLE (Extrapolation Algorithm for Greater Language-model Efficiency), a simple yet highly efficient speculative sampling framework. By incorporating a token sequence advanced by one time step, EAGLE effectively resolves the uncertainty, enabling precise second-to-top-layer feature prediction with minimal overhead. We conducted comprehensive evaluations of EAGLE, including all models from the Vicuna and LLaMA2-Chat series, the MoE model Mixtral 8x7B Instruct, and tasks in dialogue, code generation, mathematical reasoning, and instruction following. For LLaMA2-Chat 70B, EAGLE achieved a latency speedup ratio of 2.7x-3.5x, doubled throughput, while maintaining the distribution of the generated text