arXiv subjects
Publications and source records attributed to Xin Zhang.
Baxter's $T-Q$ relation for the periodic spin-$\frac12$ XYZ chain is studied. We extensively perform numerical calculations for the $T-Q$ relation and the Bethe ansatz equations. Numerical based hypotheses are then proposed to answer some open questions regarding Baxter's $T-Q$ relation and the XYZ chain.
Possible light bosonic dark matter interactions with the Standard Model photon have been searched by microwave resonant cavities. In this paper, we demonstrate the cryogenic readout system calibration of a 7.138 GHz copper cavity with a loaded quality factor $Q_l=10^4$, operated at 22 mK temperature based on a dilution refrigerator. Our readout system consists of High Electron Mobility Transistors as cryogenic amplifiers at 4 K, plus room-temperature amplifiers and a spectrum analyzer for signal power detection. We test the system with a superconducting two-level system as a single-photon source in the microwave frequency regime and report an overall 95.6 dB system gain and -71.4 dB attenuation in the cavity's input channel. The effective noise temperature of the measurement system is 7.5 K.
Quantum sensors based on solid-state defects, in particular nitrogen-vacancy (NV) centers in diamond, enable precise measurement of magnetic fields, temperature, rotation, and electric fields. However, the sensitivity of leading NV spin ensemble sensors remains far from the intrinsic spin-projection noise limit. Here we move towards this quantum limit of performance by introducing (i) a cavity quantum electrodynamic (cQED) hybrid system operating in the strong coupling regime, which enables high readout fidelity of an NV ensemble using microwave homodyne detection; (ii) a comprehensive nonlinear model of the cQED sensor operation, including NV ensemble inhomogeneity and optical polarization; and (iii) ``spin refrigeration'' where the optically-polarized spin ensemble sharply reduces the ambient-temperature microwave thermal noise, resulting in enhanced sensitivity. Applying these advances to magnetometry, we demonstrate a broadband sensitivity of 580 fT/$\sqrt{\mathrm{Hz}}$ around 15 kHz in ambient conditions. We then discuss the implications of this model for design of future magnetometers, including devices approaching 12 fT/$\sqrt{\mathrm{Hz}}$ sensitivity. Applications of these techniques extend to the fields of gyroscope and clock technologies.
For a sequence $S=(s_1, \ldots, s_k)$ of non-decreasing integers, a packing $S$-coloring of a graph $G$ is a partition of its vertex set $V(G)$ into $V_1, \ldots, V_k$ such that for every pair of distinct vertices $u,v \in V_i$, where $1 \le i \le k$, the distance between $u$ and $v$ is at least $s_i+1$. The packing chromatic number, $χ_p(G)$, of a graph $G$ is the smallest integer $k$ such that $G$ has a packing $(1,2, \ldots, k)$-coloring. Gastineau and Togni asked an open question ``Is it true that the $1$-subdivision ($D(G)$) of any subcubic graph $G$ has packing chromatic number at most $5$?'' and later Brešar, Klavžar, Rall, and Wash conjectured that it is true. In this paper, we prove that every subcubic graph has a packing $(1,1,2,2,3)$-coloring and it is sharp due to the existence of subcubic graphs that are not packing $(1,1,2,2)$-colorable. As a corollary of our result, $χ_p(D(G)) \le 6$ for every subcubic graph $G$, improving a previous bound ($8$) due to Balogh, Kostochka, and Liu in 2019, and we are now just one step away from fully solving the conjecture.
Violation of Lorentz symmetry can result in two distinct effects in the propagation of the gravitational waves (GWs). One is a modified dispersion relation and another is a frequency-dependent damping of GWs. While the former has been extensively studied in the literature, in this paper we concentrate on the frequency-dependent damping effect that arises from several specific Lorentz-violating theories, such as spatial covariant gravities, Hořava-Lifshitz gravities, etc. This Lorentz-violating damping effect changes the damping rate of GWs at different frequencies and leads to an amplitude correction to the GW waveform of compact binary inspiral systems. With this modified waveform, we then use the Fisher information matrix to investigate the prospects of constraining the Lorentz-violating damping effect with GW observations. We consider both ground-based and space-based GW detectors, including the advanced LIGO, Einstein Telescope, Cosmic Explorer (CE), Taiji, TianQin, and LISA. Our results indicate that the ground-based detectors in general give tighter constraints than those from the space-based detectors. Among the considered three ground-based detectors, CE can give the tightest constraints on the Lorentz-violating damping effect, which improves the current constraint from LIGO-Virgo-KAGRA events by about 8 times.
The Rayleigh-product channel model is utilized to characterize the rank deficiency caused by keyhole effects. However, the finite blocklength analysis for Rayleigh product channels is not available in the literature. In this paper, we will characterize the mutual information density (MID) and perform the FBL analysis to reveal the impact of rank-deficiency in Rayleigh-product channels. To this end, we first set up a central limit theorem for the MID over Rayleigh-product MIMO channels in the asymptotic regime where the number of scatterers, number of antennas, and blocklength go to infinity at the same pace. Then, we utilize the CLT to obtain the upper and lower bounds for the packet error probability, whose approximations in the high and low signal to noise ratio regimes are then derived to illustrate the impact of rank deficiency. One interesting observation is that rank-deficiency degrades the performance of MIMO systems with FBL and the fundamental limits of Rayleigh-product channels degenerate to those of the Rayleigh case when the number of scatterers approaches infinity.
Random variables $X^i$, $i=1,2$ are 'probabilistically equivalent' if they have the same law. Moreover, in any class of equivalent random variables it is easy to select canonical representatives. The corresponding questions are more involved for processes $X^i$ on filtered stochastic bases $(Ω^i, \mathcal F^i, \mathbb P^i, (\mathcal F^i_t)_{t\in [0,1]})$. Here equivalence in law does not capture relevant properties of processes such as the solutions to stochastic control or multistage decision problems. This motivates Aldous to introduce the stronger notion of synonymity based on prediction processes. Stronger still, Hoover--Keisler formalize what it means that $X^i$, $i=1,2$ have the same probabilistic properties. We establish that canonical representatives of the Hoover--Keisler equivalence classes are given precisely by the set of all Markov-martingale laws on a specific nested path space $\mathsf M_\infty$. As a consequence we obtain that, modulo Hoover--Keisler equivalence, the class of stochastic processes forms a Polish space. On this space, processes are topologically close iff they model similar probabilistic phenomena. In particular this means that their laws as well as the information encoded in the respective filtrations are similar. Importantly, compact sets of processes admit a Prohorov-type characterization. We also obtain that for every stochastic process, defined on some abstract basis, there exists a process with identical probabilistic properties which is defined on a standard Borel space.
Speech language models have significantly advanced in generating realistic speech, with neural codec language models standing out. However, the integration of human feedback to align speech outputs to human preferences is often neglected. This paper addresses this gap by first analyzing the distribution gap in codec language models, highlighting how it leads to discrepancies between the training and inference phases, which negatively affects performance. Then we explore leveraging learning from human feedback to bridge the distribution gap. We introduce SpeechAlign, an iterative self-improvement strategy that aligns speech language models to human preferences. SpeechAlign involves constructing a preference codec dataset contrasting golden codec tokens against synthetic tokens, followed by preference optimization to improve the codec language model. This cycle of improvement is carried out iteratively to steadily convert weak models to strong ones. Through both subjective and objective evaluations, we show that SpeechAlign can bridge the distribution gap and facilitating continuous self-improvement of the speech language model. Moreover, SpeechAlign exhibits robust generalization capabilities and works for smaller models. Code and models will be available at https://github.com/0nutation/SpeechGPT.
The multiple-input and multiple-output (MIMO) technique is regarded as a promising approach to boost the throughput and reliability of optical fiber communications. However, the fundamental limits of optical fiber MIMO systems with finite block-length (FBL) are not available in the literature. This paper studies the fundamental limits of optical fiber multicore/multimode systems in the FBL regime when the coding rate is a perturbation within $\mathcal{O}(\frac{1}{\sqrt{ML}})$ of the capacity, where M and L represent the number of transmit channels and blocklength, respectively. Considering the Jacobi MIMO channel, which was proposed to model the nearly lossless propagation and the crosstalks in optical fiber systems, we derive the upper and lower bounds for the optimal error probability. For that purpose, we first set up the central limit theorem for the information density in the asymptotic regime where the number of transmit, receive, available channels and the blocklength go to infinity at the same pace. The result is then utilized to derive the upper and lower bounds for the optimal average error probability with the concerned rate. The derived theoretical results reveal interesting physical insights for Jacobi MIMO channels with FBL. First, the derived bounds for Jacobi channels degenerate to those for Rayleigh channels when the number of available channels approaches infinity. Second, the high signal-to-noise (SNR) approximation indicates that a larger number of available channels results in a larger error probability. Numerical results validate the accuracy of the theoretical results and show that the derived bounds are closer to the performance of practical LDPC codes than outage probability.
In this paper, we investigate the well-posedness and ill-posedness issues for the incompressible stationary Hall-magnetohydrodynamic (Hall-MHD) system in $\mathbb{R}^3.$ We first show the existence and uniqueness of solutions provided with the forces in $\dot B^{3/p-3}_{p,r}(\mathbb{R}^3)$ for $1\leq p <3$ and $r=1$. Moreover, this result can be extended to any $1\leq r\leq \infty$ whenever $p=2,$ without any additional assumption on the physical parameters. On the other hand, we establish some ill-posedness results for Hall-MHD system by using the discontinuity of the solution mapping of the three-dimensional stationary Navier-Stokes equations in \emph{critical} function spaces $\dot{B}^{3/p-1}_{p,r}(\mathbb{R}^3)$ ($p\geq 3$).
Strong gravitational lensing is a powerful tool for investigating dark matter and dark energy properties. With the advent of large-scale sky surveys, we can discover strong lensing systems on an unprecedented scale, which requires efficient tools to extract them from billions of astronomical objects. The existing mainstream lens-finding tools are based on machine learning algorithms and applied to cut-out-centered galaxies. However, according to the design and survey strategy of optical surveys by CSST, preparing cutouts with multiple bands requires considerable efforts. To overcome these challenges, we have developed a framework based on a hierarchical visual Transformer with a sliding window technique to search for strong lensing systems within entire images. Moreover, given that multi-color images of strong lensing systems can provide insights into their physical characteristics, our framework is specifically crafted to identify strong lensing systems in images with any number of channels. As evaluated using CSST mock data based on an Semi-Analytic Model named CosmoDC2, our framework achieves precision and recall rates of 0.98 and 0.90, respectively. To evaluate the effectiveness of our method in real observations, we have applied it to a subset of images from the DESI Legacy Imaging Surveys and media images from Euclid Early Release Observations. 61 new strong lensing system candidates are discovered by our method. However, we also identified false positives arising primarily from the simplified galaxy morphology assumptions within the simulation. This underscores the practical limitations of our approach while simultaneously highlighting potential avenues for future improvements.
Air quality estimation can provide air quality for target regions without air quality stations, which is useful for the public. Existing air quality estimation methods divide the study area into disjointed grid regions, and apply 2D convolution to model the spatial dependencies of adjacent grid regions based on the first law of geography, failing to model the spatial dependencies of distant grid regions. To this end, we propose a Dual-view Supergrid-aware Graph Neural Network (DSGNN) for regional air quality estimation, which can model the spatial dependencies of distant grid regions from dual views (i.e., satellite-derived aerosol optical depth (AOD) and meteorology). Specifically, images are utilized to represent the regional data (i.e., AOD data and meteorology data). The dual-view supergrid learning module is introduced to generate supergrids in a parameterized way. Based on the dual-view supergrids, the dual-view implicit correlation encoding module is introduced to learn the correlations between pairwise supergrids. In addition, the dual-view message passing network is introduced to implement the information interaction on the supergrid graphs and images. Extensive experiments on two real-world datasets demonstrate that DSGNN achieves the state-of-the-art performances on the air quality estimation task, outperforming the best baseline by an average of 19.64% in MAE.
We consider a new cosmological model (called $\tildeΛ$CDM) in which the vacuum energy interacts with matter and radiation, and test this model using the current cosmological observations. Using the CMB+BAO+SN (CBS) dataset to constrain the model, we find that $H_0$ and $S_8$ tensions are relieved to $2.87σ$ and $2.77σ$, respectively. However, in this case, the $\tildeΛ$CDM model is not favored by the data, compared with $Λ$CDM. We find that when the $H_0$ and $S_8$ data are added to the data combination, the situation is significantly improved. In the CBS+$H_0$ case, the model relieves the $H_0$ tension to $0.47σ$, and the model is favored over $Λ$CDM. In the CBS+$H_0$+$S_8$ case, we obtain a synthetically best situation, in which the $H_0$ and $S_8$ tensions are relieved to $0.72σ$ and $2.11σ$, respectively. In this case, the model is most favored by the data. Therefore, this cosmological model can greatly relieve the $H_0$ tension and simultaneously effectively alleviate the $S_8$ tension.
Weak gravitational lensing is one of the most important probes of the nature of dark matter and dark energy. In order to extract cosmological information from next-generation weak lensing surveys (e.g., Euclid, Roman, LSST, and CSST) as much as possible, accurate measurements of weak lensing shear are required. There are existing algorithms to measure the weak lensing shear on imaging data, which have been successfully applied in previous surveys. In the meantime, machine learning (ML) has been widely recognized in various astrophysics applications in modeling and observations. In this work, we present a fully deep-learning-based approach to measuring weak lensing shear accurately. Our approach comprises two modules. The first one contains a convolutional neural network (CNN) with two branches for taking galaxy images and point spread function (PSF) simultaneously, and the output of this module includes the galaxy's magnitude, size, and shape. The second module includes a multiple-layer neural network (NN) to calibrate weak-lensing shear measurements. We name the program Forklens and make it publicly available online. Applying Forklens to CSST-like mock images, we achieve consistent accuracy with traditional approaches (such as moment-based measurement and forward model fitting) on the sources with high signal-to-noise ratios (S/N, > 20). For the sources with S/N < 10, Forklens exhibits an $\sim 36\%$ higher Pearson coefficient on galaxy ellipticity measurements. After adopting galaxy weighting, the shear measurements with Forklens deliver accuracy levels to $0.2\%$. The whole procedure of Forklens is automated and costs about $0.7$ milliseconds per galaxy, which is appropriate for adequately taking advantage of the sky coverage and depth of the upcoming weak lensing surveys.
This paper proposes PE-GPT, a custom-tailored large language model uniquely adapted for power converter modulation design. By harnessing in-context learning and specialized tiered physics-informed neural networks, PE-GPT guides users through text-based dialogues, recommending actionable modulation parameters. The effectiveness of PE-GPT is validated through a practical design case involving dual active bridge converters, supported by hardware experimentation. This research underscores the transformative potential of large language models in power converter modulation design, offering enhanced accessibility, explainability, and efficiency, thereby setting a new paradigm in the field.
A chiral coordinate Bethe ansatz method is developed to study the periodic XYZ chain. We construct a set of chiral vectors with fixed number of kinks. All vectors are factorized and have simple structures. Under roots of unity conditions, the Hilbert space has an invariant subspace and our vectors form a basis of this subspace. We propose a Bethe ansatz solely based on the action of the Hamiltonian on the chiral vectors, avoiding the use of transfer matrix techniques. This allows to parameterize the expansion coefficients and derive the homogeneous Bethe ansatz equations whose solutions give the exact energies and eigenstates. Our analytic results agree with earlier approaches, notably by Baxter, and are supported by numerical calculations.
We investigate light-matter coupling in the cuprate superconductor La$_{1.85}$Sr$_{0.15}$Cu0$_4$ (LSCO), accomplished by adhering metamaterial resonator arrays (MRAs) to a c-axis oriented single crystal. The resonators couple to the Josephson Plasma Mode (JPM) which manifests as a plasma edge in the terahertz reflectivity in the superconducting state. Terahertz reflectivity measurements at 10K reveal a renormalization of the JPM frequency, $ω_{jpm}$, from 1.7 THz for the bare crystal to $\sim$1 THz with the MRAs. With increasing temperature, the modified $ω_{jpm}$ redshifts as expected for decreasing superfluid density, vanishing above T$_{c}$. The modification of the electrodynamic response arises from resonator induced screening of the longitudinal polariton response, reminiscent of plasmon-phonon coupling in doped semiconductors. Modeling reveals that the electrodynamic response is fully interpretable using classical electromagnetism. Future studies will have to contend with the large effects we observe which could obscure subtle changes that may indicate cavity-based manipulation of superconductivity. Finally, we note that our MRA/LSCO structure is a tunable epsilon-near-zero (ENZ) metamaterial that exhibits a nonlinear response arising from the c-axis Josephson tunneling coupled with the local fields of the resonators.
Traditional analysis of highly distorted micro-X-ray diffraction (μ-XRD) patterns from hydrothermal fluid environments is a time-consuming process, often requiring substantial data preprocessing and labeled experimental data. This study demonstrates the potential of deep learning with a multitask learning (MTL) architecture to overcome these limitations. We trained MTL models to identify phase information in μ-XRD patterns, minimizing the need for labeled experimental data and masking preprocessing steps. Notably, MTL models showed superior accuracy compared to binary classification CNNs. Additionally, introducing a tailored cross-entropy loss function improved MTL model performance. Most significantly, MTL models tuned to analyze raw and unmasked XRD patterns achieved close performance to models analyzing preprocessed data, with minimal accuracy differences. This work indicates that advanced deep learning architectures like MTL can automate arduous data handling tasks, streamline the analysis of distorted XRD patterns, and reduce the reliance on labor-intensive experimental datasets.