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The Wheatstone bridge experiment is a fundamental component of the undergraduate physics curriculum, traditionally taught as a hands-on activity to explore resistance measurement and circuit balancing. This study introduces a pedagogical approach that combines qualitative symmetry-based analysis with quantitative computer-based sensitivity simulations, enhancing students' understanding and engagement. A key focus is demonstrating how balanced configurations in the Wheatstone bridge affect circuit sensitivity, providing students with an intuitive grasp of the relationship between symmetry and measurement accuracy. Using simulations, we investigate the impact of internal resistances in the galvanometer and power supply, showing that lower resistances increase the circuit's sensitivity to minor resistance changes. Additionally, various resistor configurations are analyzed, highlighting the effect of careful adjustments in achieving maximal sensitivity. A Bayesian optimization-based software tool was developed to guide students in selecting optimal component values, thereby minimizing the need for manual adjustments while ensuring accurate measurements. This integrated approach bridges traditional experimentation with computational techniques, fostering critical thinking and preparing students for modern scientific practices. The study demonstrates that this enriched methodology significantly enhances the learning experience, equipping students with valuable skills in both experimental and computational aspects of physics.

An asymptotically flat hairy black hole (HBH) can exhibit distinct characteristics when compared to the Schwarzschild black hole, due to the evasion of no-hair theorem by minimally coupling the Einstein gravity with a scalar potential which possesses asymmetric vacua, i.e, a false vacuum $(\phi=0)$ and a true vacuum $(\phi=\phi_1)$. In this paper, we investigate the geodesic motion of both massive test particles and photons in the vicinity of HBH with $\phi_1=0.5$ and $\phi_1=1.0$ by analyzing their effective potentials derived from the geodesic equation. By fixing $\phi_1$, the effective potential of a massive test particle increases monotonically when its angular momentum $L$ is very small. When $L$ increases to a critical value, the effective potential possesses an inflection point which is known as the innermost stable of circular orbit (ISCO), where the test particle can still remain stable in a circular orbit with a minimal radius without being absorbed by the HBH or fleeing to infinity. Beyond the critical value of $L$, the effective potential possesses a local minimum and a local maximum, indicating the existence of unstable and stable circular orbits, respectively. Moreover, the HBH possesses an unstable photon sphere but its location slightly deviates from the Schwarzschild black hole. The trajectories of null geodesics in the vicinity of HBH can also be classified into three types, which are the direct, lensing and photon sphere, based on the deflection angle of light, but the values of impact parameters can vary significantly than the Schwarzschild black hole., Comment: 11 pages with total 11 figures

Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Despite some progress in this field, linear-in-temperature resistance and inverse-in-frequency tail of optical conductivity are unresolved issues in non-Fermi liquids. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistance.

In recent years, Large language model-powered Automated Program Repair (LAPR) techniques have achieved state-of-the-art bug-fixing performance and have been pervasively applied and studied in both industry and academia. Nonetheless, LLMs were proved to be highly sensitive to input prompts, with slight differences in the expressions of semantically equivalent programs potentially causing repair failures. Therefore, it is crucial to conduct robustness testing on LAPR techniques before their practical deployment. However, related research is scarce. To this end, we propose MT-LAPR, a Metamorphic Testing framework exclusively for LAPR techniques, which summarizes nine widely-recognized Metamorphic Relations (MRs) by developers across three perturbation levels: token, statement, and block. Afterward, our proposed MRs are applied to buggy codes to generate test cases, which are semantically equivalent yet to affect the inference of LAPR. Experiments are carried out on two extensively examined bug-fixing datasets, i.e., Defect4J and QuixBugs, and four bug-fixing abled LLMs released recently, demonstrating that 34.4% - 48.5% of the test cases expose the instability of LAPR techniques on average, showing the effectiveness of MT-LAPR and uncovering a positive correlation between code readability and the robustness of LAPR techniques. Inspired by the above findings, this paper uses the test cases generated by MT-LAPR as samples to train a CodeT5-based code editing model aiming at improving code readability and then embeds it into the LAPR workflow as a data preprocessing step. Extensive experiments demonstrate that this approach significantly enhances the robustness of LAPR by 49.32% at most.

A stellar-mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) is generally considered to be the central engine of gamma-ray bursts (GRBs). Neutrinos escaping from the disk will annihilate out of the disk to produce the fireball that could power GRBs with blackbody (BB) components. The initial GRB jet power and fireball launch radius are related to the annihilation luminosity and annihilation height of the NDAFs, respectively. In this paper, we collect 7 GRBs with known redshifts and identified BB components to test whether the NDAF model works. We find that, in most cases, the values of the accretion rates and the central BH properties are all in the reasonable range, suggesting that these BB components indeed originate from the neutrino annihilation process., Comment: 8 pages, 1 table, 1 figure, accepted for publication in ApJ

In 2007, \'A. Baricz put forward a conjecture concerning Tur\'an-type inequalities for Gaussian hypergeometric functions (see Conjecture \ref{ConjA} in Section \ref{Sec1}). In this paper, the authors disprove this conjecture with several methods, and present Tur\'an-type double inequalities for Gaussian hypergeometric functions, and sharp bounds for complete and generalized elliptic integrals of the first kind., Comment: 23 pages

Quantum computing holds immense potential for addressing a myriad of intricate challenges, which is significantly amplified when scaled to thousands of qubits. However, a major challenge lies in developing an efficient and scalable quantum control system. To address this, we propose a novel Hierarchical MicroArchitecture (HiMA) designed to facilitate qubit scaling and exploit quantum process-level parallelism. This microarchitecture is based on three core elements: (i) discrete qubit-level drive and readout, (ii) a process-based hierarchical trigger mechanism, and (iii) multiprocessing with a staggered triggering technique to enable efficient quantum process-level parallelism. We implement HiMA as a control system for a 72-qubit tunable superconducting quantum processing unit, serving a public quantum cloud computing platform, which is capable of expanding to 6144 qubits through three-layer cascading. In our benchmarking tests, HiMA achieves up to a 4.89x speedup under a 5-process parallel configuration. Consequently, to the best of our knowledge, we have achieved the highest CLOPS (Circuit Layer Operations Per Second), reaching up to 43,680, across all publicly available platforms.

The Janis-Newman-Winicour (JNW) spacetime possesses a naked singularity, although it represents an exact particle-like solution to the Einstein-Klein-Gordon theory with a massless scalar field. Here, we investigate the possible formation of a naked singularity in the JNW spacetime, using the thin-shell approximation to describe the gravitational collapse. By introducing different matter contents to construct thin-shells, we demonstrate the impossibility of naked singularity formation during the gravitational collapse unless the causality or null energy condition of the thin-shell is violated. Therefore, the weak cosmic censorship is satisfied even with the naked singularity of the JNW spacetime., Comment: 13 pages, 6 figures

In the NISQ era, achieving large-scale quantum computing demands compact circuits to mitigate decoherence and gate error accumulation. Quantum operations with diverse degrees of freedom hold promise for circuit compression, but conventional approaches encounter challenges in simultaneously adjusting multiple parameters. Here, we propose a transition composite gate (TCG) scheme grounded on state-selective transition path engineering, enabling more expressive conditional operations. We experimentally validate a controlled unitary (CU) gate as an example, with independent and continuous parameters. By adjusting the parameters of $\rm X^{12}$ gate, we obtain the CU family with a fidelity range of 95.2% to 99.0% leveraging quantum process tomography (QPT). To demonstrate the capability of circuit compression, we use TCG scheme to prepare 3-qubit Greenberger-Horne-Zeilinger (GHZ) and W states, with the fidelity of 96.77% and 95.72%. TCG can achieve the reduction in circuit depth of about 40% and 44% compared with the use of CZ gates only. Moreover, we show that short-path TCG (SPTCG) can further reduce the state-preparation circuit time cost. The TCG scheme exhibits advantages in certain quantum circuits and shows significant potential for large-scale quantum algorithms., Comment: 21 pages, 12 figures

An accurate map of intracellular organelle pH is crucial for comprehending cellular metabolism and organellar functions. However, a unified intracellular pH spectrum using a single probe is still lack. Here, we developed a novel quantum entanglement-enhanced pH-sensitive probe called SITE-pHorin, which featured a wide pH-sensitive range and ratiometric quantitative measurement capabilities. Subsequently, we measured the pH of various organelles and their sub-compartments, including mitochondrial sub-spaces, Golgi stacks, endoplasmic reticulum, lysosomes, peroxisomes, and endosomes in COS-7 cells. For the long-standing debate on mitochondrial compartments pH, we measured the pH of mitochondrial cristae as 6.60 \pm 0.40, the pH of mitochondrial intermembrane space as 6.95 \pm 0.30, and two populations of mitochondrial matrix pH at approximately 7.20 \pm 0.27 and 7.50 \pm 0.16, respectively. Notably, the lysosome pH exhibited a single, narrow Gaussian distribution centered at 4.79 \pm 0.17. Furthermore, quantum chemistry computations revealed that both the deprotonation of the residue Y182 and the discrete curvature of deformed benzene ring in chromophore are both necessary for the quantum entanglement mechanism of SITE-pHorin. Intriguingly, our findings reveal an accurate pH gradient (0.6-0.9 pH unit) between mitochondrial cristae and matrix, suggesting prior knowledge about \Delta pH (0.4-0.6) and mitochondrial proton motive force (pmf) are underestimated., Comment: 64 pages, 7 figures, the supplemental material contains 13 supplemental figures and 4 supplemental tables

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than $0.2\%$, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science., Comment: 31 pages, 10 figures

This paper assumes that neutrino flavor conversion is induced by right-handed neutrino mixture via seesaw mechanism, which leads to apparent fake neutrino mixture with neutrino mass eigenstate consistent with flavor state of left-handed neutrino rather than mixture of flavor state. The transition probability between right-handed neutrinos due to mixture can be explained well by boson intermediating flavor flip interaction between right-handed neutrinos and neutrino oscillation can be considered macro phenomenon before all flavor flip interactions arrive at balance.

Previously, a class of regular and asymptotically flat gravitating scalar solitons (scalarons) has been constructed in the Einstein--Klein--Gordon (EKG) theory by adopting a phantom field with Higgs-like potential where the kinetic term has the wrong sign and the scalaron possesses the negative Arnowitt--Deser--Misner (ADM) mass as a consequence. In this paper, we demonstrate that the use of the phantom field can be avoided by inverting the Higgs-like potential in the EKG system when the kinetic term has a proper sign, such that the corresponding gravitating scalaron can possess the positive ADM mass. We systematically study the basic properties of the gravitating scalaron, such as the ADM mass, the energy conditions, the geodesics of test particles, etc. Moreover, we find that it can be smoothly connected to the counterpart hairy black hole solutions from our recent work in the small horizon limit., Comment: 18 pages with 9 figures. Special Issue of the Universe (MDPI): Compact Objects (invited contribution)

Active galactic nucleus (AGN) disks are widely considered potential hosts for various high-energy transients, including gamma-ray bursts (GRBs). The reactivation of GRB central engines can provide additional energy to shocks formed during the interaction of the initially ejected GRB jets with the circumburst material, commonly referred to as energy injections. In this paper, we study GRBs occurring in AGN disks within the context of energy injections. We adopt the standard external forward shock (EFS) model and consider both short- and long-duration GRB scenarios. Light curves for two types of radiation, namely the radiation from the heated disk material (RHDM) and GRB afterglows, are computed. We find that the energy injection facilitates the EFS to break out from the photosphere of the low-density AGN disk at relativistic velocity. Moreover, the energy injection almost does not affect the RHDM but significantly enhances the peak flux of the GRB afterglows., Comment: 12 pages, 6 figures, 2 tables, accepted for publication in ApJ

We investigate scalarized black holes in the Einstein-minimally coupled scalar theory with a negative potential $V(\phi)=-\alpha^2\phi^6$. The tachyonic instability is absent from analyzing the linearized scalar equation, which could not allow for spontaneous scalarization. However, we obtain the black hole solutions with scalar hair by solving three full equations because this scalar potential violates the weak energy condition. This shows clearly that scalarized black holes can be obtained without introducing a non-minimal scalar coupling term. We perform the stability analysis for scalarized black holes by adopting radial perturbations, implying that all scalarized black holes belonging to a single branch are unstable., Comment: 18 pages with 8 figures (To match with the published version)

High-performance catalysts are crucial for sustainable energy conversion and human health. However, the discovery of catalysts faces challenges due to the absence of efficient approaches to navigating vast and high-dimensional structure and composition spaces. In this study, we propose a high-throughput computational catalyst screening approach integrating density functional theory (DFT) and Bayesian Optimization (BO). Within the BO framework, we propose an uncertainty-aware atomistic machine learning model, UPNet, which enables automated representation learning directly from high-dimensional catalyst structures and achieves principled uncertainty quantification. Utilizing a constrained expected improvement acquisition function, our BO framework simultaneously considers multiple evaluation criteria. Using the proposed methods, we explore catalyst discovery for the CO2 reduction reaction. The results demonstrate that our approach achieves high prediction accuracy, facilitates interpretable feature extraction, and enables multicriteria design optimization, leading to significant reduction of computing power and time (10x reduction of required DFT calculations) in high-performance catalyst discovery.

The study of strongly correlated fermionic systems, crucial for understanding condensed matter physics, has been significantly advanced by numerical computational methods. Among these, the Determinant Quantum Monte Carlo (DQMC) method stands out for its ability to provide exact numerical solutions. However, the computational complexity of DQMC, particularly in dealing with large system sizes and the notorious sign problem, limits its applicability. We introduce an innovative approach to enhance DQMC efficiency through the implementation of submatrix updates. Building upon the foundational work of conventional fast updates and delay updates, our method leverages a generalized submatrix update algorithm to address challenges in simulating strongly correlated fermionic systems with both onsite and extended interactions at both finite and zero temperatures. We demonstrate the method's superiority by comparing it with previous update methods in terms of computational complexity and efficiency. Specifically, our submatrix update method significantly reduces the computational overhead, enabling the simulation of system sizes up to 8,000 sites without pushing hard. This advancement allows for a more accurate determination of the finite temperature phase diagram of the 3D Hubbard model at half-filling. Our findings not only shed light on the phase transitions within these complex systems but also pave the way for more effective simulations of strongly correlated electrons, potentially guiding experimental efforts in cold atom simulations of the 3D Hubbard model., Comment: 18 pages, 12 figures, 3 tables, note added

Residual entropy, indicative of the degrees of freedom in a system at absolute zero, is a cornerstone for understanding quantum and classical ground states. Despite its critical role in elucidating low-temperature phenomena and ground state degeneracy, accurately quantifying residual entropy remains a formidable challenge due to significant computational hurdles. In this Letter, we introduce the Temperature Incremental Monte Carlo (TIMC) method, our novel solution crafted to surmount these challenges. The TIMC method incrementally calculates the partition function ratio of neighboring temperatures within Monte Carlo simulations, enabling precise entropy calculations and providing insights into a spectrum of other temperature-dependent observables in a single computational sweep of temperatures. We have rigorously applied TIMC to a variety of complex systems, such as the frustrated antiferromagnetic Ising model on both C60 and 2D triangular lattices, the Newman-Moore spin glass model, and a 2D quantum transverse field Ising model. Notably, our method surmounts the traditional obstacles encountered in partition function measurements when mapping $d$-dimensional quantum models to $d+1$-dimensional classical counterparts. The TIMC method's finesse in detailing entropy across the entire temperature range enriches our comprehension of critical phenomena in condensed matter physics. This includes insights into spin glasses, phases exhibiting spontaneous symmetry breaking, topological states of matter and fracton phases. Our approach not only advances the methodology for probing the entropic landscape of such systems but also paves the way for exploring their broader thermodynamic and quantum mechanical properties., Comment: 5 pages, 5 figures

The dependence of Natural Language Processing (NLP) intelligent software on Large Language Models (LLMs) is increasingly prominent, underscoring the necessity for robustness testing. Current testing methods focus solely on the robustness of LLM-based software to prompts. Given the complexity and diversity of real-world inputs, studying the robustness of LLMbased software in handling comprehensive inputs (including prompts and examples) is crucial for a thorough understanding of its performance. To this end, this paper introduces RITFIS, a Robust Input Testing Framework for LLM-based Intelligent Software. To our knowledge, RITFIS is the first framework designed to assess the robustness of LLM-based intelligent software against natural language inputs. This framework, based on given threat models and prompts, primarily defines the testing process as a combinatorial optimization problem. Successful test cases are determined by a goal function, creating a transformation space for the original examples through perturbation means, and employing a series of search methods to filter cases that meet both the testing objectives and language constraints. RITFIS, with its modular design, offers a comprehensive method for evaluating the robustness of LLMbased intelligent software. RITFIS adapts 17 automated testing methods, originally designed for Deep Neural Network (DNN)-based intelligent software, to the LLM-based software testing scenario. It demonstrates the effectiveness of RITFIS in evaluating LLM-based intelligent software through empirical validation. However, existing methods generally have limitations, especially when dealing with lengthy texts and structurally complex threat models. Therefore, we conducted a comprehensive analysis based on five metrics and provided insightful testing method optimization strategies, benefiting both researchers and everyday users.

Many-body entanglement unveils additional aspects of quantum matter and offers insights into strongly correlated physics. While ground-state entanglement has received much attention in the past decade, the study of mixed-state quantum entanglement using negativity in interacting fermionic systems remains largely unexplored. We demonstrate that the partially transposed density matrix of interacting fermions, similar to their reduced density matrix, can be expressed as a weighted sum of Gaussian states describing free fermions, enabling the calculation of rank-$n$ R\'{e}nyi negativity within the determinant quantum Monte Carlo framework. We conduct the first calculation of the rank-two R\'{e}nyi negativity for the half-filled Hubbard model and the spinless $t$-$V$ model. Our calculation reveals that the area law coefficient of the R\'{e}nyi negativity for the spinless $t$-$V$ model has a logarithmic finite-size scaling at the finite-temperature transition point. Our work contributes to the calculation of entanglement and sets the stage for future studies on quantum entanglement in various fermionic many-body mixed states., Comment: 8+10 pages, 3+2 figures

The Blandford-Znajek (BZ) mechanism in stellar-mass black hole (BH) hyperaccretion systems is generally considered to power gamma-ray bursts (GRBs). Based on observational GRB data, we use the BZ mechanism driven by the BH hyperaccretion disc to investigate the evolution of the BH mass and spin after the jets break out from the progenitors. We find that the BH growths are almost independent of initial BH masses. Meanwhile, the BH growths will be more efficient with smaller initial spin parameters. We conclude that (i) the BZ mechanism is efficient for triggering BH growths for only 1 of 206 typical long-duration GRBs; (ii) the mean BH mass growths of ultra-long GRBs are marginal for all 7 samples collected; (iii) for the short-duration GRBs, the results that BHs show minimal growths is consistent with the mass supply limitation in the scenario of compact object mergers., Comment: 12 pages, 3 figures, 3 tables, accepted for publication in MNRAS

Non-perturbative contributions of the Euclidean path integral are important to understand the information loss paradox. In this paper, we revisit the Yang-Mills instantons in the Einstein-Yang-Mills theory. There exists a globally regular solution that is known as the Bartnik-McKinnon solution and a black hole solution. The regular and the black hole solutions are smoothly connected in the small horizon limit. Their Euclidean action is solely characterized by the ADM mass, and the transition probability follows the usual Bekenstein-Hawking entropy formula. Therefore, the Yang-Mills instantons provide a non-perturbative channel to the black hole evaporation, which competes effectively with perturbative processes, and becomes dominant toward the end of evaporation. We show that these instantons provide a smooth transition mechanism from a black hole to regular spacetime., Comment: 17 pages, 5 figures

We investigate the role of superconducting phase fluctuations in generic 2D superconductors. For nodal d-wave superconductors, it is found that the thermal (static) phase fluctuations in the normal state significantly broaden the d-wave nodes, and lead to the pseudogap and accompanying Fermi arcs in a quite general manner. The formation of Fermi arcs can be depicted by the intertwinement between d-wave superconductivity and the scattering of Cooper pairs. To support our theoretical findings, we numerically report the observation of Fermi arcs in a concrete lattice model, proposed originally by X. Y. Xu and T. Grover in Phys. Rev. Lett. 126, 217002 (2021), using the determinant quantum Monte Carlo (DQMC) method without the infamous sign problem. As far as we noticed, it is the first time in a highly-correlated model that the Fermi arcs are identified with unbiased DQMC simulations. Despite the conciseness of our theory, our simulation results confirm the theoretical predictions qualitatively., Comment: 6 pages, 5 figures for the main text; 8 pages, 5 figures for the supplementary material

Many Transformer-based pre-trained models for code have been developed and applied to code-related tasks. In this paper, we review the existing literature, examine the suitability of model architectures for different tasks, and look at the generalization ability of models on different datasets, and their resource consumption. We examine three very representative pre-trained models for code: CodeBERT, CodeGPT, and CodeT5, and conduct experiments on the top-4 most targeted software engineering tasks that we found in our literature survey: Code Summarization, Bug Fixing, Bug Detection, and Code Search. In our study, we showcase the capability of decoder-only models (CodeGPT) for specific generation tasks under state-of-the-art evaluation metrics and contest the common belief that the encoder-decoder architecture is optimal for general-purpose coding tasks. Additionally, we found that the most frequently used models are not necessarily the most suitable for certain applications and the developers' needs are not adequately addressed by current research. As well, we found that the benchmark and frequent dataset for Bug Fixing and Code Summarization both fail to enable models to generalize onto other datasets for the same task (the frequent dataset refers to the dataset with the highest frequency used in literature other than the benchmark). We use statistical testing to support our conclusions from experiments. Finally, CodeBERT is highly efficient for understanding tasks, whereas CodeT5's efficiency for generation tasks is in doubt, as the highest resource consumption does not guarantee a consistent better performance on different metrics. We also discuss the numerous practical issues in advancing future research on transformer-based models for code-related tasks.