arXiv subjects
Publications and source records attributed to Jing Zhou.
The partition function of the topological twisted super Yang-Mills field theory on the boundary can be expanded as Jones polynomial, which can be computed as expectation values of Wilson loop operators. We show that the zero of the Jones polynomial is Lee-Yang type. Moreover, Lee-Yang phase transition is also discussed in the Jones polynomial of torus knot and the topological twisted super Yang-Mills field theory.
In this paper we show an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realised as a square billiard with a periodically oscillating platform. We use normal forms to describe how the energy changes in a period and we employ techniques for hyperbolic systems with singularities to show the exponential drift of these normal forms on a divided time-energy phase.
With the development of quantum many-body simulator, Hamiltonian tomography has become an increasingly important technique for verification of quantum devices. Here we investigate recovering the Hamiltonians of two spin chains with 2-local interactions and 3-local interactions by measuring local observables. For these two models, we show that when the chain length reaches a certain critical number, we can recover the local Hamiltonian from its one steady state by solving the homogeneous operator equation (HOE) developed in Ref. [1]. To explain the existence of such a critical chain length, we develop an alternative method to recover Hamiltonian by solving the energy eigenvalue equations (EEE). By using the EEE method, we completely recovered the numerical results from the HOE method. Then we theoretically prove the equivalence between the HOE method and the EEE method. In particular, we obtain the analytical expression of the rank of the constraint matrix in the HOE method by using the EEE method, which can be used to determine the correct critical chain length in all the cases.
GaN-based lateral Schottky diodes (SBDs) have attracted great attention for high-power applications due to its combined high electron mobility and large critical breakdown field. However, the breakdown voltage (BV) of the SBDs are far from exploiting the material advantages of GaN at present, limiting the desire to use GaN for ultra-high voltage (UHV) applications. Then, a golden question is whether the excellent properties of GaN-based materials can be practically used in the UHV field? Here we demonstrate UHV AlGaN/GaN SBDs on sapphire with a BV of 10.6 kV, a specific on-resistance of 25.8 mΩ.cm2, yielding a power figure of merit of more than 3.8 GW/cm2. These devices are designed with single channel and 85-μm anode-to-cathode spacing, without other additional electric field management, demonstrating its great potential for the UHV application in power electronics.
We make two observations on the motion of coupled particles in a periodic potential. Coupled pendula, or the space-discretized sine-Gordon equation is an example of this problem. Linearized spectrum of the synchronous motion turns out to have a hidden asymptotic periodicity in its dependence on the energy; this is the gist of the first observation. Our second observation is the discovery of a special property of the purely sinusoidal potentials: the linearization around the synchronous solution is equivalent to the classical Lamè equation. As a consequence, {\it all but one instability zones of the linearized equation collapse to a point for the one-harmonic potentials}. This provides a new example where Lamé's finite zone potential arises in the simplest possible setting.
Localized surface plasmons (LSPs) have played a significant role in improving the light emission efficiency of light emitting diodes (LEDs). In this report, polygonal nanoholes have been fabricated in the p-GaN layer of InGaN-based LEDs by using Ni nanoporous film as the etching mask, and then Au/Al metal nanoparticles are embedded in the nanoholes to form the LSP structure. The coupling between the LSP and the LED has been clearly observed. The results show that the light output of the LEDs has been increased by 46% at higher current injection condition, and together with a shift of the gain peak position to the LSP peak resonance energy. As the coupling distance is decreased from 60 nm to 30 nm, the maximum enhancement factor increases to 2.38. The above results indicate that the LSP from the polygonal metal nanoparticles is a kind of very promising structure to enhance the lighting performance of the InGaN-based LEDs.
We investigate design and performance of communications over the bandlimited Gaussian channel with one-bit output quantization. A transceiver structure is proposed, which generates the channel input using a finite set of time-limited and approximately bandlimited waveforms, and performs oversampling on the channel output by an integrate-and-dump filter preceding the one-bit quantizer. The waveform set is constructed based on a specific bandlimited random process with certain zero-crossing properties which can be utilized to convey information. In the presence of the additive white Gaussian noise, a discrete memoryless channel model of our transceiver is derived. Consequently, we determine a closed-form expression for the high signal-to-noise-ratio (SNR) asymptotic information rate of the transceiver, which can be achieved by independent and identically distributed input symbols. By evaluating the fractional power containment bandwidth, we further show that at high SNR, the achievable spectral efficiency grows roughly logarithmically with the oversampling factor, coinciding with a notable result in the absence of noise [19]. Moreover, the error performance of our transceiver is evaluated by low density parity check coded modulation. Numerical results demonstrate that reliable communication at rates exceeding one bit per Nyquist interval can be achieved at moderate SNR.
We study the polaron problem of an impurity immersed in a dissipative spin-orbit coupled Fermi gas via a non-self-consistent T-matrix method. We first propose an experimental scheme to realize a spin-orbit coupled Fermi bath with dissipation, and show that such a system can be described by a non-Hermitian Hamiltonian that contains an imaginary spin-flip term and an imaginary constant shift term. We find that the non-Hermiticity will change the single particle dispersion of the bath gas, and modify the properties of attractive and repulsive polarons such as energy, quasi-particle residue, effective mass, and decay rate. We also investigate the Thouless criteria corresponding to the instability of the polaron molecule transition, which suggests a molecule state is more facilitated with stronger bath dissipation. Finally, we consider the case with finite impurity density and calculate the interaction between polarons. Our result extends the study of polaron physics to non-Hermitian systems and may be realized in future experiment.
We study the effect of magnetic field on heavy quark-antiquark pair in both Einstein-Maxwell(EM) and Einstein-Maxwell-Dilaton(EMD) model. The interquark distance, free energy, entropy, binding energy and internal energy of the heavy quarkonium are calculated. It is found that the free energy suppresses and the entropy increases quickly with the increase of the magnetic field $B$. The binding energy vanishes at smaller distance when increasing the magnetic field, which indicates the quark-antiquark pair dissociates at smaller distance. The internal energy which consists of free energy and entropy will increase at large separating distance for non-vanishing magnetic field. These conclusions are consistent both in the EM and EMD model. Moreover, we also find that the quarkonium will dissociate easier in the parallel direction than that in the transverse direction for EMD model, but the conclusion is opposite in EM model. Lattice results are in favor of EMD model. Besides, a Coulomb-plus-linear potential(Cornell potential) can be realized only in EMD model. Thus, a dilaton field is proved to be important in holographic model. Finally, we also show that the free energy, entropy and internal energy of a single quark in EMD model with the presence of magnetic field.
A major issue in Smoothed Particle Hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High-frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a Vorticity Refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot-Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods.
To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However, they struggle to accurately reproduce the probability distribution function (PDF) in the input space from that in the latent space. If the embedding were isometric, this issue can be solved, because the relation of PDFs can become tractable. To achieve isometric property, we propose Rate- Distortion Optimization guided autoencoder inspired by orthonormal transform coding. We show our method has the following properties: (i) the Jacobian matrix between the input space and a Euclidean latent space forms a constantlyscaled orthonormal system and enables isometric data embedding; (ii) the relation of PDFs in both spaces can become tractable one such as proportional relation. Furthermore, our method outperforms state-of-the-art methods in unsupervised anomaly detection with four public datasets.
In this paper, we consider a class of nonconvex complex quadratic programming (CQP) problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first derive a new enhanced semidefinite relaxation (SDR) for problem (CQP). Based on the newly derived SDR, we further propose an efficient branch-and-bound algorithm for solving problem (CQP). Key features of our proposed algorithm are: (1) it is guaranteed to find the global solution of the problem (within any given error tolerance); (2) it is computationally efficient because it carefully utilizes the special structure of the problem. We apply our proposed algorithm to solve the multi-input multi-output (MIMO) detection problem, the unimodular radar code design problem, and the virtual beamforming design problem. Simulation results show that our proposed enhanced SDR, when applied to the above problems, is generally much tighter than the conventional SDR and our proposed global algorithm can efficiently solve these problems. In particular, our proposed algorithm significantly outperforms the state-of-the-art sphere decode algorithm for solving the MIMO detection problem in the hard cases (where the number of inputs and outputs is equal or the SNR is low) and a state-of-the-art general-purpose global optimization solver called Baron for solving the virtual beamforming design problem.
In this letter, we demonstrate high-performance lateral AlGaN/GaN Schottky barrier diodes (SBD) on Si substrate with a recessed-anode structure. The optimized rapid etch process provides results in improving etching quality with a 0.26-nm roughness of the anode recessed surface. By using the high work function metal Pt as the Schottky electrode, a low Von of 0.71 V is obtained with a high uniformity of 0.023 V for 40 devices. Supported by the flat anode recess surface and related field plate design, the SBD device with the anode-cathode spacing of 15 um show the Ron,sp of 1.53 mOhm.cm2 only, the breakdown voltage can reach 1592 V with a high power FOM (Figure-of-Merit) of 1656 MW/cm2. For the SBD device with the anode-cathode spacing of 30 um, the breakdown voltage can be as high as 2521 V and the power FOM is 1244 MW/cm2.
We demonstrate an anomalous spin-orbit torque induced by the broken magnetic symmetry in the antiferromagnet IrMn. We study the magnetic structure of three phases of IrMn thin films using neutron diffraction technique. The magnetic mirror symmetry M' is broken laterally in both L10-IrMn and L12-IrMn3 but not γ-IrMn3. We observe an out-of-plane damping-like spin-orbit torque in both L10-IrMn/permalloy and L12-IrMn3/permalloy bilayers but not in γ-IrMn3/permalloy. This is consistent with both the symmetry analysis on the effects of a broken M' on spin-orbit torque and the theoretical predictions of the spin Hall effect and the Rashba-Edelstein effect. In addition, the measured spin-orbit torque efficiencies are 0.61+-0.01, 1.01+-0.03 and 0.80+-0.01 for the L10, L12 and γ phases, respectively. Our work highlights the critical roles of the magnetic asymmetry in spin-orbit torque generation.
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory identifies equivalence between model-averaged and composite quantile estimation. However, little to nothing is known about such equivalence between methods that encourage sparsity. This paper provides a toolbox to further study robustness in these settings and focuses on prediction. In particular, we study optimally weighted model-averaged as well as composite $l_1$-regularized estimation. Optimal weights are determined by minimizing the asymptotic mean squared error. This approach incorporates the effects of regularization, without the assumption of perfect selection, as is often used in practice. Such weights are then optimal for prediction quality. Through an extensive simulation study, we show that no single method systematically outperforms others. We find, however, that model-averaged and composite quantile estimators often outperform least-squares methods, even in the case of Gaussian model noise. Real data application witnesses the method's practical use through the reconstruction of compressed audio signals.
The freedom of fast iterations of distributed deep learning tasks is crucial for smaller companies to gain competitive advantages and market shares from big tech giants. HorovodRunner brings this process to relatively accessible spark clusters. There have been, however, no benchmark tests on HorovodRunner per se, nor specifically graph convolutional network (GCN, hereafter), and very limited scalability benchmark tests on Horovod, the predecessor requiring custom built GPU clusters. For the first time, we show that Databricks' HorovodRunner achieves significant lift in scaling efficiency for the convolutional neural network (CNN, hereafter) based tasks on both GPU and CPU clusters, but not the original GCN task. We also implemented the Rectified Adam optimizer for the first time in HorovodRunner.
Deep learning based image compression methods have achieved superior performance compared with transform based conventional codec. With end-to-end Rate-Distortion Optimization (RDO) in the codec, compression model is optimized with Lagrange multiplier $λ$. For conventional codec, signal is decorrelated with orthonmal transformation, and uniform quantizer is introduced. We propose a variable rate image compression method with dead-zone quantizer. Firstly, the autoencoder network is trained with RaDOGAGA \cite{radogaga} framework, which can make the latents isometric to the metric space, such as SSIM and MSE. Then the conventional dead-zone quantization method with arbitrary step size is used in the common trained network to provide the flexible rate control. With dead-zone quantizer, the experimental results show that our method performs comparably with independently optimized models within a wide range of bitrate.
Two-dimensional (2D) transition metal dichalcogenides (TMDs) based photodetectors have shown great potential for the next generation optoelectronics. However, most of the reported MoS2 photodetectors function under the photogating effect originated from the charge-trap mechanism, which is difficult for quantitative control. Such devices generally suffer from a poor compromise between response speed and responsivity (R) and large dark current. Here, a dual-gated (DG) MoS2 phototransistor operating based on the interface coupling effect (ICE) is demonstrated. By simultaneously applying a negative top-gate voltage (VTG) and positive back-gate voltage (VBG) to the MoS2 channel, the photo-generated holes can be effectively trapped in the depleted region under TG. An ultrahigh R of ~1E5 A/W and detectivity (D*) of ~1E14 Jones have been achieved in several devices with different thickness under Pin of 53 uW/cm2 at VTG=-5 V. Moreover, the response time of the DG phototransistor can also be modulated based on the ICE. Based on these systematic measurements of MoS2 DG phototransistors, the results show that the ICE plays an important role in the modulation of photoelectric performances. Our results also pave the way for the future optoelectrical application of 2D TMDs materials and prompt for further investigation in the DG structured phototransistors.