Out-of-Time-Order Correlation at a Quantum Phase Transition

In this paper we numerically calculate the out-of-time-order correlation functions in the one-dimensional Bose-Hubbard model. Our study is motivated by the conjecture that a system with Lyapunov exponent saturating the upper bound $2\pi/\beta$ will have a holographic dual to a black hole at finite temperature. We further conjecture that for a many-body quantum system with a quantum phase transition, the Lyapunov exponent will have a peak in the quantum critical region where there exists an emergent conformal symmetry and is absent of well-defined quasi-particles. With the help of a relation between the R\'enyi entropy and the out-of-time-order correlation function, we argue that the out-of-time-order correlation function of the Bose-Hubbard model will also exhibit an exponential behavior at the scrambling time. By fitting the numerical results with an exponential function, we extract the Lyapunov exponents in the one-dimensional Bose-Hubbard model across the quantum critical regime at finite temperature. Our results on the Bose-Hubbard model support the conjecture. We also compute the butterfly velocity and propose how the echo type measurement of this correlator in the cold atom realizations of the Bose-Hubbard model without inverting the Hamiltonian.Comment: 7 pages, 6 figures, published versio

Out-of-Time-Order Correlation for Many-Body Localization

In this paper we first compute the out-of-time-order correlators (OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second R\'enyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.Comment: 6 pages, 3 figures, published versio

An investigation of mechanics in nanomachining of Gallium Arsenide

The first two decades of the 21st Century have seen a wide exploitation of Gallium Arsenide (GaAs) in photoemitter device, microwave devices, hall element, solar cell, wireless communication as well as quantum computation device due to its superior material properties, such as higher temperature resistance, higher electronic mobility and energy gap that outperforms silicon. Ultra-precision multiplex two dimensional (2D) or three dimensional (3D) free-form nanostructures are often required on GaAs-based devices, such as radio frequency power amplifiers and switches used in the 5G smart mobile wireless communication. However, GaAs is extremely difficult to machine as its elastic modulus, Knoop hardness and fracture toughness are lower than other semiconductor materials such as silicon and germanium. This PhD thesis investigated the mechanics of nanomachining of GaAs through molecular dynamics (MD) simulation combined with single point diamond turning (SPDT) and atomic force microscope (AFM) based experimental characterization in order to realise ductile-regime nanomachining of GaAs, which is the most important motivation behind this thesis. The investigation of mechanics of nanomachining of GaAs included studies on cutting temperature, cutting forces, origin ductile plasticity, atomic scale friction, formation mechanism of sub-surface damage, wear mechanism of diamond cutting tool. Machinability of GaAs at elevated temperature was also studied in order to develop thermally-assisted nanomachining process in the future to facilitate plastic material deformation and removal. This thesis contributed to address the knowledge gaps such as what is the incipient plasticity, how does the sub-surface damage form and how does the diamond cutting tool wear during nanomachining of GaAs. Firstly, this thesis investigated the cutting zone temperature, cutting forces and origin of plasticity of GaAs material, including single crystal GaAs and polycrystalline GaAs during SPDT process. The experimental and MD simulation study showed GaAs has a strong anisotropic machinability. The simulation results indicated that the deformation of polycrystalline GaAs is accompanied by dislocation nucleation in the grain boundaries (GBs) leading to the initiation of plastic deformation. Furthermore, the 1/2 is the main type of dislocation responsible for ductile plasticity in polycrystalline GaAs. A phenomenon of fluctuation from wave crests to wave troughs in the cutting forces was only observed during cutting of polycrystalline GaAs, not for single-crystal GaAs. Secondly, this thesis studied the atomic scale friction during AFM-based nanomachining process. a strong size effect was observed when the scratch depths are below 2 nm in MD simulations and 15 nm from the AFM experiments respectively. A strong quantitative corroboration was obtained between the MD simulations and the AFM experiments in the specific scratch energy and more qualitative corroboration with the pile up and the kinetic coefficient of friction. This conclusion suggested that the specific scratch energy is insensitive to the tool geometry and the speed of scratch used in this investigation but the pile up and kinetic coefficient of friction are dependent on the geometry of the tool tip. Thirdly, this thesis investigated formation mechanism of sub-surface damage and wear mechanism of diamond cutting tool during nanomachining of GaAs. Transmission Electron Microscope (TEM) measurement of sub-surface of machined nanogrooves on GaAs and MD simulation of dislocation movement indicated the dual slip mechanisms i.e. shuffle-set slip mechanism and glide-set slip mechanism, and the creation of dislocation loops, multi dislocation nodes, and dislocation junctions governed the formation mechanism of sub-surface damage of GaAs during nanomachining process. Elastic-plastic deformation at the apex of the diamond tip was observed in MD simulations. Meanwhile, a transition of the diamond tip from its initial cubic diamond lattice structure sp3 hybridization to graphite lattice structure sp2 hybridization was revealed. Graphitization was, therefore, found to be the dominant wear mechanism of the diamond tip during nanometric cutting of single crystal GaAs. Finally, in MD simulations study of cutting performance at elevated temperature, hotter conditions resulted in the reduction of cutting forces by 25% however, the kinetic coefficient of friction went up by about 8%. While material removal rate was found to increase with the increase of the substrate temperature, it was accompanied by an increase of the sub-surface damage in the substrate. Moreover, a phenomenon of chip densification was found to occur during hot cutting which referred to the fact that the amorphous cutting chips obtained from cutting at low temperature will have lower density than the chips obtained from cutting at higher temperatures.The first two decades of the 21st Century have seen a wide exploitation of Gallium Arsenide (GaAs) in photoemitter device, microwave devices, hall element, solar cell, wireless communication as well as quantum computation device due to its superior material properties, such as higher temperature resistance, higher electronic mobility and energy gap that outperforms silicon. Ultra-precision multiplex two dimensional (2D) or three dimensional (3D) free-form nanostructures are often required on GaAs-based devices, such as radio frequency power amplifiers and switches used in the 5G smart mobile wireless communication. However, GaAs is extremely difficult to machine as its elastic modulus, Knoop hardness and fracture toughness are lower than other semiconductor materials such as silicon and germanium. This PhD thesis investigated the mechanics of nanomachining of GaAs through molecular dynamics (MD) simulation combined with single point diamond turning (SPDT) and atomic force microscope (AFM) based experimental characterization in order to realise ductile-regime nanomachining of GaAs, which is the most important motivation behind this thesis. The investigation of mechanics of nanomachining of GaAs included studies on cutting temperature, cutting forces, origin ductile plasticity, atomic scale friction, formation mechanism of sub-surface damage, wear mechanism of diamond cutting tool. Machinability of GaAs at elevated temperature was also studied in order to develop thermally-assisted nanomachining process in the future to facilitate plastic material deformation and removal. This thesis contributed to address the knowledge gaps such as what is the incipient plasticity, how does the sub-surface damage form and how does the diamond cutting tool wear during nanomachining of GaAs. Firstly, this thesis investigated the cutting zone temperature, cutting forces and origin of plasticity of GaAs material, including single crystal GaAs and polycrystalline GaAs during SPDT process. The experimental and MD simulation study showed GaAs has a strong anisotropic machinability. The simulation results indicated that the deformation of polycrystalline GaAs is accompanied by dislocation nucleation in the grain boundaries (GBs) leading to the initiation of plastic deformation. Furthermore, the 1/2 is the main type of dislocation responsible for ductile plasticity in polycrystalline GaAs. A phenomenon of fluctuation from wave crests to wave troughs in the cutting forces was only observed during cutting of polycrystalline GaAs, not for single-crystal GaAs. Secondly, this thesis studied the atomic scale friction during AFM-based nanomachining process. a strong size effect was observed when the scratch depths are below 2 nm in MD simulations and 15 nm from the AFM experiments respectively. A strong quantitative corroboration was obtained between the MD simulations and the AFM experiments in the specific scratch energy and more qualitative corroboration with the pile up and the kinetic coefficient of friction. This conclusion suggested that the specific scratch energy is insensitive to the tool geometry and the speed of scratch used in this investigation but the pile up and kinetic coefficient of friction are dependent on the geometry of the tool tip. Thirdly, this thesis investigated formation mechanism of sub-surface damage and wear mechanism of diamond cutting tool during nanomachining of GaAs. Transmission Electron Microscope (TEM) measurement of sub-surface of machined nanogrooves on GaAs and MD simulation of dislocation movement indicated the dual slip mechanisms i.e. shuffle-set slip mechanism and glide-set slip mechanism, and the creation of dislocation loops, multi dislocation nodes, and dislocation junctions governed the formation mechanism of sub-surface damage of GaAs during nanomachining process. Elastic-plastic deformation at the apex of the diamond tip was observed in MD simulations. Meanwhile, a transition of the diamond tip from its initial cubic diamond lattice structure sp3 hybridization to graphite lattice structure sp2 hybridization was revealed. Graphitization was, therefore, found to be the dominant wear mechanism of the diamond tip during nanometric cutting of single crystal GaAs. Finally, in MD simulations study of cutting performance at elevated temperature, hotter conditions resulted in the reduction of cutting forces by 25% however, the kinetic coefficient of friction went up by about 8%. While material removal rate was found to increase with the increase of the substrate temperature, it was accompanied by an increase of the sub-surface damage in the substrate. Moreover, a phenomenon of chip densification was found to occur during hot cutting which referred to the fact that the amorphous cutting chips obtained from cutting at low temperature will have lower density than the chips obtained from cutting at higher temperatures

Extreme Gradient Boosting (XGBoost) Model for Vehicle Trajectory Prediction in Connected and Autonomous Vehicle Environment

Connected and autonomous vehicles (CAVs) have the ability to receive information on their leading vehicles through multiple sensors and vehicle-to-vehicle (V2V) technology and then predict their future behaviour thus to improve roadway safety and mobility. This study presents an innovative algorithm for connected and autonomous vehicles to determine their trajectory considering surrounding vehicles. For the first time, the XGBoost model is developed to predict the acceleration rate that the object vehicle should take based on the current status of both the object vehicle and its leading vehicle. Next Generation Simulation (NGSIM) datasets are utilised for training the proposed model. The XGBoost model is compared with the Intelligent Driver Model (IDM), which is a prior state-of-the-art model. Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are applied to evaluate the two models. The results show that the XGBoost model outperforms the IDM in terms of prediction errors. The analysis of the feature importance reveals that the longitudinal position has the greatest influence on vehicle trajectory prediction results

Deep sequencing of the microRNA expression in fall dormant and non-dormant alfalfa

AbstractMicroRNAs (miRNAs) play a critical role in post-transcriptional gene regulation that down-regulates target genes by mRNA degradation or translational repression. Evidence is increasing for their crucial roles during plant development. Identification of miRNAs at the global genome-level by high-throughput sequencing is essential to functionally characterize miRNAs in plants. Alfalfa (Medicago sativa L.) is one of the most widely cultivated perennial forage legumes worldwide. Fall dormancy is an adaptive character related to the biomass production and winter survival in alfalfa. However, little is known about miRNA-mediated developmental regulation of fall dormancy in alfalfa. Here, we provide detailed experimental methods and analysis pipeline in our study to identify miRNAs that were responsive to fall dormancy (Fan W et al., Genome-wide identification of different dormant Medicago sativa L. microRNAs in response to fall dormancy, submitted for publication) for reproducible research. The data generated in our work provide meaningful information for understanding the roles of miRNAs in response to seasonal change and growth regulation in alfalfa