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Quantum control allows a wide range of quantum operations employed in molecular physics, nuclear magnetic resonance and quantum information processing. Thanks to the existing microelectronics industry, semiconducting qubits, where quantum information is encoded in spin or charge degree freedom of electrons or nuclei in semiconductor quantum dots, constitute a highly competitive candidate for scalable solid-state quantum technologies. In quantum information processing, advanced control techniques are needed to realize quantum manipulations with both high precision and noise resilience. In this review, we first introduce the basics of various widely-used control methods, including resonant excitation, adabatic passage, shortcuts to adiabaticity, composite pulses, and quantum optimal control. Then we review the practical aspects in applying these methods to realize accurate and robust quantum gates for single semiconductor qubits, such as Loss-DiVincenzo spin qubit, spinglet-triplet qubit, exchange-only qubit and charge qubit.

We compute the fragmentation function of a light quark into S-wave fully-charmed tetraquarks ($T_{4c}$) within the nonrelativistic QCD (NRQCD) framework, at leading order in $\alpha_{s}$ and $v$. We present results for light quark fragmentation into $T_{4c}$ and predict its contribution to $T_{4c}$ production at high transverse momentum ($p_{T}$) at the LHC and EIC. We also compare light quark fragmentation with charm quark and gluon fragmentation channels. Our analysis shows that the production cross section for $T_{4c}$ from light quark fragmentation is smaller than that from gluon fragmentation but larger than that from charm quark fragmentation., Comment: 14 pages, 3 figures, 2 tables

3D Gaussian Splatting (3DGS) allows flexible adjustments to scene representation, enabling continuous optimization of scene quality during dense visual simultaneous localization and mapping (SLAM) in static environments. However, 3DGS faces challenges in handling environmental disturbances from dynamic objects with irregular movement, leading to degradation in both camera tracking accuracy and map reconstruction quality. To address this challenge, we develop an RGB-D dense SLAM which is called Gaussian Splatting SLAM in Dynamic Environments (Gassidy). This approach calculates Gaussians to generate rendering loss flows for each environmental component based on a designed photometric-geometric loss function. To distinguish and filter environmental disturbances, we iteratively analyze rendering loss flows to detect features characterized by changes in loss values between dynamic objects and static components. This process ensures a clean environment for accurate scene reconstruction. Compared to state-of-the-art SLAM methods, experimental results on open datasets show that Gassidy improves camera tracking precision by up to 97.9% and enhances map quality by up to 6%., Comment: This paper is currently under reviewed for ICRA 2025

Blockchain interoperability protocols enable cross-chain asset transfers or data retrievals between isolated chains, which are considered as the core infrastructure for Web 3.0 applications such as decentralized finance protocols. However, existing protocols either face severe scalability issues due to high on-chain and off-chain costs, or suffer from trust concerns because of centralized designs. In this paper, we propose \texttt{MAP}, a trustless blockchain interoperability protocol that relays cross-chain transactions across heterogeneous chains with high scalability. First, within \texttt{MAP}, we develop a novel \textit{cross-chain relay} technique, which integrates a unified relay chain architecture and on-chain light clients of different source chains, allowing the retrieval and verification of diverse cross-chain transactions. Furthermore, we reduce cross-chain verification costs by incorporating an optimized zk-based light client scheme that adaptively decouples signature verification overheads from inefficient smart contract execution and offloads them to off-chain provers. For experiments, we conducted the first large-scale evaluation on existing interoperability protocols. With \texttt{MAP}, the required number of on-chain light clients is reduced from $O(N^2)$ to $O(N)$, with around 35\% reduction in on-chain costs and 25\% reduction for off-chain costs when verifying cross-chain transactions. To demonstrate the effectiveness, we deployed \texttt{MAP} in the real world. By 2024, we have supported over six popular public chains, 50 cross-chain applications and relayed over 200K cross-chain transactions worth over 640 million USD. Based on rich practical experiences, we constructed the first real-world cross-chain dataset to further advance blockchain interoperability research.

Scaling laws for critical phenomena take pivotal status in almost all branches of physics. However, as scaling laws are commonly guaranteed by the renormalization group theory, systems that violate them have rarely been found. In this letter, we demonstrate that gravitational system can break scaling laws. We derive this result through investigating phase transition and critical phenomenon in a gravitational system with quantum anomaly. For the first time, we outline the key conditions to violate the scaling laws in generic gravitational system viewed from the equation of state $P=P(T,V)$. Our results indicate that quantum effects can magnify the distinctiveness of gravity, which may be significant to understand the microscopic structure of spacetime., Comment: 7 pages, 3 figures

Blockchain oracle is a critical third-party web service for Decentralized Finance (DeFi) protocols. Oracles retrieve external information such as token prices from exchanges and feed them as trusted data sources into smart contracts, enabling core DeFi applications such as loaning protocols. Currently, arithmetic mean based time-weighted average price (TWAP) oracles are widely used in DeFi by averaging external price data with fixed time frame, which is considered reliable and gas-efficient for protocol execution. However, recent research shows that TWAP price feeds are vulnerable to price manipulation attack even with long time frame setting, which would further introduce long time delays and price errors hindering the service quality of DeFi applications. To address this issue, we propose a novel on-chain gas-efficient pricing algorithm (Ormer) that heuristically estimates the median of the current streaming asset price feed based on a piecewise-parabolic formula, while the time delay is suppressed by fusing estimations with different observation window size. Our evaluation based on Ethereum WETH/USDT swapping pair price feed shows that Ormer reduces the mean absolute price error by 15.3% and the time delay by 49.3% compared to TWAP. For gas efficiency, an optimized smart contract design and constant storage requirement regardless of the number of price observations is developed for Ormer.

With the advent of high-precision nanoscale lithography technology, high-resolution image sensing has experienced rapid development in recent years. Currently, mainstream commercial image sensors predominantly utilize Bayer array color filters to implement RGB colorful imaging strategies. However, as pixel sizes transition into the submicron dimensions, traditional dye filters used in image sensors have long been hampered by limited optical efficiency, suboptimal signal-to-noise ratios, and significant difficulties in miniaturization. In this work, a novel 4-channel RGB-IR color router for image sensing, distinct from the traditional absorption-transmission mechanisms, was proposed through inverse design methodologies. Utilizing genetic algorithms and DCGAN models, approximately 20,000 random color routing structures were generated and trained. From these, an optimized spectral splitting structure with a minimal periodic size of 1.6 um * 1.6 um was identified. This structure achieves peak optical efficiencies 1.7 times greater than those of dye filters, while also offering superior color imaging quality and signal intensity. This innovative design approach, leveraging deep learning integration, demonstrates an on-chip strategy for color realization in 4-channel image sensors, and holds significant promise for enhancing the development of next-generation high-performance image sensing chip systems., Comment: 19 pages,5 figures

Scaling up quantum dots to two-dimensional (2D) arrays is a crucial step for advancing semiconductor quantum computation. However, maintaining excellent tunability of quantum dot parameters, including both nearest-neighbor and next-nearest-neighbor couplings, during 2D scaling is challenging, particularly for silicon quantum dots due to their relatively small size. Here, we present a highly controllable and interconnected 2D quantum dot array in planar silicon, demonstrating independent control over electron fillings and the tunnel couplings of nearest-neighbor dots. More importantly, we also demonstrate the wide tuning of tunnel couplings between next-nearest-neighbor dots,which plays a crucial role in 2D quantum dot arrays. This excellent tunability enables us to alter the coupling configuration of the array as needed. These results open up the possibility of utilizing silicon quantum dot arrays as versatile platforms for quantum computing and quantum simulation.

Electron spin qubits in silicon are a promising platform for fault-tolerant quantum computing. Low-frequency noise, including nuclear spin fluctuations and charge noise, is a primary factor limiting gate fidelities. Suppressing this noise is crucial for high-fidelity qubit operations. Here, we report on a two-qubit quantum device in natural silicon with universal qubit control, designed to investigate the upper limits of gate fidelities in a non-purified Si/SiGe quantum dot device. By employing advanced device structures, qubit manipulation techniques, and optimization methods, we have achieved single-qubit gate fidelities exceeding 99% and a two-qubit Controlled-Z (CZ) gate fidelity of 91%. Decoupled CZ gates are used to prepare Bell states with a fidelity of 91%, typically exceeding previously reported values in natural silicon devices. These results underscore that even natural silicon has the potential to achieve high-fidelity gate operations, particularly with further optimization methods to suppress low-frequency noise.

The dynamic pricing problem of a freeway corridor with high-occupancy toll (HOT) lanes was formulated and solved based on a point queue abstraction of the traffic system [Yin and Lou, 2009]. However, existing pricing strategies cannot guarantee that the closed-loop system converges to the optimal state, in which the HOT lanes' capacity is fully utilized but there is no queue on the HOT lanes, and a well-behaved estimation and control method is quite challenging and still elusive. This paper attempts to fill the gap by making three fundamental contributions: (i) to present a simpler formulation of the point queue model based on the new concept of residual capacity, (ii) to propose a simple feedback control theoretic approach to estimate the average value of time and calculate the dynamic price, and (iii) to analytically and numerically prove that the closed-loop system is stable and guaranteed to converge to the optimal state, in either Gaussian or exponential manners., Comment: 34 pages, 16 figures

A stable dynamic pricing scheme is essential to guarantee the desired performance of high-occupancy-toll (HOT) lanes, where single-occupancy vehicles (SOVs) can pay a price to use the HOT lanes. But existing methods apply to either only one type of lane-choice models with unknown parameters or different types of lane-choice models but with known parameters. In this study we present a new dynamic pricing scheme that is stable and applies to different types of lane-choice models with unknown parameters. There are two operational objectives for operating HOT lanes: (i) to maintain the free-flow condition to guarantee the travel time reliability; and (ii) to maximize the HOT lanes' throughput to minimize the system's total delay. The traffic dynamics on both HOT and general purpose (GP) lanes are described by point queue models, where the queueing times are determined by the demands and capacities. We consider three types of lane-choice models: the multinomial logit model when SOVs share the same value of time, the vehicle-based user equilibrium model when SOVs' values of time are heterogeneous and follow a distribution, and a general lane-choice model. We demonstrate that the second objective is approximately equivalent to the social welfare optimization principle for the logit model. Observing that the dynamic price and the excess queueing time on the GP lanes are linearly correlated in all the lane-choice models, we propose a feedback control method to determine the dynamic prices based on two integral controllers. We further present a method to estimate the parameters of a lane-choice model once its type is known. Analytically we prove that the equilibrium state of the closed-loop system with constant demand patterns is ideal, since the two objectives are achieved in it, and that it is asymptotically stable. With numerical examples we verify the effectiveness of the solution method., Comment: 24 pages, 10 figures

The Rapid and accurate identification of Gamma-Ray Bursts (GRBs) is crucial for unraveling their origins. However, current burst search algorithms frequently miss low-threshold signals or lack universality for observations. In this study, we propose a novel approach utilizing transfer learning experiment based on convolutional neural network (CNN) to establish a universal GRB identification method, which validated successfully using GECAM-B data. By employing data augmentation techniques, we enhance the diversity and quantity of the GRB sample. We develop a 1D CNN model with a multi-scale feature cross fusion module (MSCFM) to extract features from samples and perform classification. The comparative results demonstrated significant performance improvements following pre-training and transferring on a large-scale dataset. Our optimal model achieved an impressive accuracy of 96.41% on the source dataset of GECAM-B, and identified three previously undiscovered GRBs by contrast with manual analysis of GECAM-B observations. These innovative transfer learning and data augmentation methods presented in this work hold promise for applications in multi-satellite exploration scenarios characterized by limited data sets and a scarcity of labeled samples in high-energy astronomy., Comment: 17 pages, 7 figures

Deconfined quantum critical points (DQCPs) are proposed as unconventional second-order phase transitions beyond the Landau-Ginzburg-Wilson paradigm. The nature and experimental realizations of DQCPs are crucial issues of importance. We illustrate the potential for DQCPs between the valence bond solid state and the antiferromagnetic phase to arise in optical lattices containing frustrated dipolar bosons subject to hard-core constraints. The emergence of DQCPs is comprehended through the fusion of two Berezinskii-Kosterlitz-Thouless (BKT) transitions. The DQCPs and the BKTs are confirmed by the finite-size scaling of ground-state fidelity susceptibilities. The numerical analysis reveals varying critical exponents of the correlation length in DQCPs and the logarithmic scaling in BKTs, respectively. This work offers a promising platform for realizing DQCPs and provides valuable insights into their nature within the framework of topological phase transitions., Comment: 9 pages, 8 figures

Type I gamma-ray bursts (GRBs) are believed to originate from compact binary merger usually with duration less than 2 seconds for the main emission. However, recent observations of GRB 211211A and GRB 230307A indicate that some merger-origin GRBs could last much longer. Since they show strikingly similar properties (indicating a common mechanism) which are different from the classic "long"-short burst (e.g. GRB 060614), forming an interesting subclass of type I GRBs, we suggest to name them as type IL GRBs. By identifying the first peak of GRB 230307A as a quasi-thermal precursor, we find that the prompt emission of type IL GRB is composed of three episodes: (1) a precursor followed by a short quiescent (or weak emission) period, (2) a long-duration main emission, and (3) an extended emission. With this burst pattern, a good candidate, GRB 170228A, was found in the Fermi/GBM archive data, and subsequent temporal and spectral analyses indeed show that GRB 170228A falls in the same cluster with GRB 211211A and GRB 230307A in many diagnostic figures. Thus this burst pattern could be a good reference for rapidly identifying type IL GRB and conducting low-latency follow-up observation. We estimated the occurrence rate and discussed the physical origins and implications for the three emission episodes of type IL GRBs. Our analysis suggests the pre-merger precursor model, especially the super flare model, is more favored for type IL GRBs.

In this study, we explore the quantum critical phenomena in generalized Aubry-Andr\'{e} models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-Andr\'{e} model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments., Comment: 9 pages, 5 figures

We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological $\theta$ angle of $\pi$. Introducing rhombic SIA shifts this angle from $\pi$, resulting in $y$- and $x$-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological $\theta$ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators., Comment: 12 pages, 8 figures

Inspired by the recent observation of the Higgs boson radiative decay into $Z^0$ by {\tt ATLAS} and {\tt CMS} Collaborations, we investigate the next-to-leading-order (NLO) electroweak correction to this rare decay process in Standard Model (SM). Implementing the on-shell renormalization scheme, we find that the magnitude of the NLO electroweak correction may reach $7\%$ of the leading order (LO) prediction, much more significant than that of the NLO QCD correction, which is merely about $0.3\%$. After incorporating the ${\cal O}(\alpha)$ correction, the predicted partial width from various $\alpha$ schemes tend to converge to each other. Including both NLO electroweak and QCD corrections, the SM prediction for the branching fraction shifts from the LO value of $(1.40-1.71)\times 10^{-3}$ to $(1.55\pm 0.06)\times 10^{-3}$, considerably lower than the measured value ${\cal B}_{\rm exp}[H\to Z^0\gamma]=(3.4\pm 1.1)\times 10^{-3}$. Resolving this alarming discrepancy clearly calls for further theoretical investigations, and, more importantly, experimental efforts from {\tt HL-LHC} and the prospective Higgs factories such as {\tt CEPC} and {\tt FCC-ee}., Comment: 7 pages, 2 figures, 1 table; Matching the published version in PRD Letter

Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an $S$-wave fully-charmed tetraquark, denoted as $T_{4c}$. The charm-to-$T_{4c}$ fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in $\alpha_{s}$ expansion. The LDMEs are approximated using the $T_{4c}$ four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-$T_{4c}$ fragmentation function, we predict the $T_{4c}$ production rate at high transverse momentum $p_T$ regime in colliders. %After implementing appropriate kinematic constraints, Both the differential distribution over $p_T$ and the integrated cross sections are predicted at the \texttt{LHC}. The cross sections for $T_{4c}$ states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for $T_{4c}$ event production at the \texttt{LHC}. Additionally, we estimate for the photoproduction of $T_{4c}$ in electron-proton ($ep$) collisions. It is observed that the cross sections for these processes are moderate at the \texttt{HERA} and \texttt{EIC}, and relatively small at the \texttt{EicC}. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at $ep$ colliders is somewhat challenging., Comment: 22 pages, 2 figures, 4 tables; significant enhancement aligns with the published edition

The automotive industry is transitioning from traditional ECU-based systems to software-defined vehicles. A central role of this revolution is played by containers, lightweight virtualization technologies that enable the flexible consolidation of complex software applications on a common hardware platform. Despite their widespread adoption, the impact of containerization on fundamental real-time metrics such as end-to-end latency, communication jitter, as well as memory and CPU utilization has remained virtually unexplored. This paper presents a microservice architecture for a real-world autonomous driving application where containers isolate each service. Our comprehensive evaluation shows the benefits in terms of end-to-end latency of such a solution even over standard bare-Linux deployments. Specifically, in the case of the presented microservice architecture, the mean end-to-end latency can be improved by 5-8 %. Also, the maximum latencies were significantly reduced using container deployment.

By using the Fermi/Gamma-ray Burst Monitor data of the X-ray bursts (XRBs) of SGR J1935+2154, we investigate the temporal clustering of the bursts and the cumulative distribution of the waiting time and fluence/flux. It is found that the bursts occurring in the episode hosting FRB 20200428 have obviously shorter waiting times than those in the other episodes. The general statistical properties of the XRBs further indicate they could belong to a self-organized critical (SOC) system (e.g., starquakes), making them very similar to the earthquake phenomena. Then, according to a unified scaling law between the waiting time and energy of the earthquakes as well as their aftershocks, we implement an analogy analysis on the XRBs and find that the FRB episode owns more dependent burst events than the other episodes. It is indicated that the fast radio burst (FRB) emission could be produced by the interaction between different burst events, which could correspond to a collision between different seismic/Alfven waves or different explosion outflows. Such a situation could appear when the magnetar enters into a global intensive activity period.

The control of flying qubits carried by itinerant photons is ubiquitous in quantum networks. Beside their logical states, the shape of flying qubits must also be tailored for high-efficiency information transmission. In this paper, we introduce quantum optimal control theory to the shaping of flying qubits. Building on the flying-qubit control model established in our previous work, we design objective functionals for the generation of shaped flying qubits under practical constraints on the emitters and couplers. Numerical simulations employing gradient-descent algorithms demonstrate that the optimized control can effectively mitigate unwanted level and photon leakage caused by these non-idealities. Notably, while coherent control offers limited shaping capacity with a fixed coupler, it can significantly enhance the shaping performance when combined with a tunable coupler that has restricted tunability. The proposed optimal control framework provides a systematic approach to achieving high-quality control of flying qubits using realistic quantum devices., Comment: 12 pages, 8 figures

Repetitive Ramsey interferometry measurements (RIMs) are often used to measure qubit coherence, assuming that the environment remains unaffected after each measurement and the outcomes of all measurements are independent and identically distributed (i.i.d.). While this assumption is valid for a classical environment, it may not hold for a quantum environment due to the non-negligible backaction from qubit to environment. Here we present a general theoretical framework to incorporate the measurement backaction from qubit to environment in sequential RIMs. We show that a RIM of a qubit induces a quantum channel on the quantum environment, and sequential RIMs gradually steer the quantum environment to the fixed points of the channel. We reveal three distinct environment steering effects -- polarization, depolarization and metastable polarization, depending on the commutativity of the noise operator $B$ and the free environment Hamiltonian $H_e$: (1) if $B$ commutes with $H_e$, i.e., $[B,H_e]=0$, the quantum environment is gradually polarized to different eigenstates of $B$ as the number $m$ of repetitive RIMs increases; (2) When $[B,H_e]\neq 0$, the quantum environment is gradually depolarized to a maximally mixed state of its whole Hilbert space or a Hilbert subspace; (3) When $[B,H_e]\neq 0$ but one of $H_e$ and $B$ is a small perturbation on the other, metastable polarization can happen, such that the quantum environment is first polarized for a finite range of $m$ but becomes gradually depolarized as $m$ increases further. The environment steering also makes the measurement statistics of sequential RIMs develop non-i.i.d. features, such that the measurement result distribution can display multiple peaks for a small quantum environment, corresponding to different fixed points of the quantum channel.

Achieving precise preparation of quantum many-body states is crucial for the practical implementation of quantum computation and quantum simulation. However, the inherent challenges posed by unavoidable excitations at critical points during quench processes necessitate careful design of control fields. In this work, we introduce a promising and versatile dynamic control neural network tailored to optimize control fields. We address the problem of suppressing defect density and enhancing cat-state fidelity during the passage across the critical point in the quantum Ising model. Our method facilitates seamless transitions between different objective functions by adjusting the {optimization strategy}. In comparison to gradient-based power-law quench methods, our approach demonstrates significant advantages for both small system sizes and long-term evolutions. We provide a detailed analysis of the specific forms of control fields and summarize common features for experimental implementation. Furthermore, numerical simulations demonstrate the robustness of our proposal against random noise and spin number fluctuations. The optimized defect density and cat-state fidelity exhibit a transition at a critical ratio of the quench duration to the system size, coinciding with the quantum speed limit for quantum evolution., Comment: 14 pages, 9 figures; Accepted in Phys. Rev. A

Gamma-ray bursts (GRBs) are believed to launch relativistic jets, which generate prompt emission by internal processes, and produce long-lasting afterglows by driving external shocks into surrounding medium. However, how the jet powers the external shock is poorly known. The unprecedented observations of the keV-MeV emission with GECAM and the TeV emission with LHAASO of the brightest-of-all-time GRB 221009A offer a great opportunity to study the prompt-to-afterglow transition and the impact of jet on the early dynamics of external shock. In this letter, we find that the cumulative light curve of keV-MeV emission could well fit the rising stage of the TeV light curve of GRB 221009A, with a time delay, $4.45^{+0.26}_{-0.26}$\,s, of TeV emission. Moreover, both the rapid increase in the initial stage and the excess from about \T+260\,s to 270\,s in the TeV light curve are tracking the light-curve bumps in the prompt keV-MeV emission. The close relation between the keV-MeV and TeV emission reveals the continuous energy-injection into the external shock. Assuming an energy-injection rate exactly following the keV-MeV flux of GRB 221009A, including the very early precursor, we build a continuous energy-injection model where the jet Lorentz factor is derived from the TeV time delay, and the TeV data is well fitted, with the TeV excesses interpreted by inverse Compton (IC) scatterings of the inner-coming prompt emission by the energetic electrons in external shock., Comment: ApJL accepted version; analytical derivation of SSC flux scaling with shock energy added

In this paper, we investigate the gauge dependence of various physical observables in the quantum Rabi model (QRM) under different potential fields, arising from the Hilbert-space truncation of the atomic degree of freedom. We discover that in both the square-well potential and oscillator potential,the optimal gauges for the ground-state energy of the QRM vary with respect to the cavity frequency, with the dipole gauge being optimal in the low-frequency limit and the Coulomb gauge in the high-frequency limit of the cavity frequency. Additionally, for higher energy levels, the optimal gauge asymptotically approaches the dipole gauge. However, for the dynamical quantity out-time-order correlator (OTOC), we find the necessity to introduce an optimal dynamical gauge. We determine the optimal dynamical gauge by minimizing the mean error between the two-level OTOC and the full Hamiltonian one. We expect that this study will contribute to a more profound understanding of the subtle relation between gauge choice and the dynamics of QED systems.

The quantum Rabi model (QRM) is a fundamental model for light-matter interactions. A fascinating feature of the QRM is that it manifests a quantum phase transition which is applicable for critical quantum metrology (CQM). Effective application for CQM needs the exact location of the transition point, however the conventional expression for the transition coupling is only valid in the extreme limit of low frequency, while apart from zero frequency an accurate location is still lacking. In the present work we conversely use the quantum Fisher information (QFI) in the CQM to identify the transition coupling, which finds out that transition coupling indeed much deviates from the conventional one once a finite frequency is turned on. Polaron picture is applied to analytically reproduce the numeric QFI. An accurate expression for the transition coupling is obtained by the inspiration from the fractional-power-law effect of polaron frequency renormalization. From the QFI in the polaron picture we find that the transition occurs around a point where the effective velocity and the susceptibility of the single-photon absorption rate reach maximum. Our result provides an accurate reference of transition couplings for quantum metrology at non-zero frequencies. The formulation of the QFI in the polaron picture also prepares an analytic method with an accurate compensation for the parameter regime difficult to access for the numerics. Besides the integer/fractional power law analysis to extract the underlying physics of transition, the QFI/velocity relation may also add some insight in bridging the QFI and transition observables., Comment: 14 pages, 8 figures

This paper presents an adaptive online learning framework for systems with uncertain parameters to ensure safety-critical control in non-stationary environments. Our approach consists of two phases. The initial phase is centered on a novel sparse Gaussian process (GP) framework. We first integrate a forgetting factor to refine a variational sparse GP algorithm, thus enhancing its adaptability. Subsequently, the hyperparameters of the Gaussian model are trained with a specially compound kernel, and the Gaussian model's online inferential capability and computational efficiency are strengthened by updating a solitary inducing point derived from new samples, in conjunction with the learned hyperparameters. In the second phase, we propose a safety filter based on high-order control barrier functions (HOCBFs), synergized with the previously trained learning model. By leveraging the compound kernel from the first phase, we effectively address the inherent limitations of GPs in handling high-dimensional problems for real-time applications. The derived controller ensures a rigorous lower bound on the probability of satisfying the safety specification. Finally, the efficacy of our proposed algorithm is demonstrated through real-time obstacle avoidance experiments executed using both a simulation platform and a real-world 7-DOF robot.

This paper proposes a LiDAR-based goal-seeking and exploration framework, addressing the efficiency of online obstacle avoidance in unstructured environments populated with static and moving obstacles. This framework addresses two significant challenges associated with traditional dynamic control barrier functions (D-CBFs): their online construction and the diminished real-time performance caused by utilizing multiple D-CBFs. To tackle the first challenge, the framework's perception component begins with clustering point clouds via the DBSCAN algorithm, followed by encapsulating these clusters with the minimum bounding ellipses (MBEs) algorithm to create elliptical representations. By comparing the current state of MBEs with those stored from previous moments, the differentiation between static and dynamic obstacles is realized, and the Kalman filter is utilized to predict the movements of the latter. Such analysis facilitates the D-CBF's online construction for each MBE. To tackle the second challenge, we introduce buffer zones, generating Type-II D-CBFs online for each identified obstacle. Utilizing these buffer zones as activation areas substantially reduces the number of D-CBFs that need to be activated. Upon entering these buffer zones, the system prioritizes safety, autonomously navigating safe paths, and hence referred to as the exploration mode. Exiting these buffer zones triggers the system's transition to goal-seeking mode. We demonstrate that the system's states under this framework achieve safety and asymptotic stabilization. Experimental results in simulated and real-world environments have validated our framework's capability, allowing a LiDAR-equipped mobile robot to efficiently and safely reach the desired location within dynamic environments containing multiple obstacles.

In this study, we explore an approach aimed at enhancing the transmission or reflection coefficients of absorbing materials through the utilization of joint measurements of entangled photon states. On the one hand, through the implementation of photon catalysis in the reflected channel, we can effectively modify the state of the transmission channel, leading to a notable improvement in the transmission ratio. Similarly, this approach holds potential for significantly amplifying the reflection ratio of absorbing materials, which is useful for detecting cooperative targets. On the other hand, employing statistical counting methods based on the technique of heralding on zero photons, we evaluate the influence of our reflection enhancement protocol for detecting noncooperative targets, which is validated through Monte Carlo simulations of a quantum radar setup affected by Gaussian white noise. Our results demonstrate a remarkable enhancement in the signal-to-noise ratio of imaging, albeit with an increase in mean-square error. These findings highlight the potential practical applications of our approach in the implementation of quantum radar., Comment: 11 pages, 10 figures

We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen--Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.

Metastability in open system dynamics describes the phenomena of initial relaxation to longlived metastable states before decaying to the asymptotic stable states. It has been predicted in continuous-time stochastic dynamics of both classical and quantum systems. Here we present a general theory of metastability in discrete-time open quantum dynamics, described by sequential quantum channels. We focus on a general class of quantum channels on a target system, induced by an ancilla system with a pure-dephasing coupling to the target system and under Ramsey sequences. Interesting metastable behaviors are predicted and numerically demonstrated by decomposing the average dynamics into stochastic trajectories. Examples and applications are also discussed., Comment: 7 pages, 2 figures (+9 pages, 5 figures supplement)

Understanding the nature of repeating fast radio bursts (FRBs) is crucial to probe their underlying physics. In this work, we analyze the waiting time statistics between bursts of three repeating FRBs from four datasets. We find a universally pronounced dependency of the waiting times on the previous time interval (denoted as $\lambda_0$). We observe a temporal clustering where short waiting times tend to be followed by short ones, and long by long comparative to their mean value. This memory dependency is manifested in the conditional mean waiting time as well as in the conditional mean residual time to the next burst, both of which increase in direct proportion to $\lambda_0$. Consequently, the likelihood of experiencing a subsequent FRB burst within a given time window after the preceding burst is generally influenced by the burst history. We reveal that for the first time, these memory effects are present in the scale-invariant preconditioned waiting time distribution. We show that the memory effect provides a unified description of waiting times which may account for both the repeating FRBs and the apparent non-repeating FRBs (i.e. only observed one time). These results shed new light on the mechanism of FRBs.

In this work, we investigate the inclusive photoproduction of the $C$-odd, $S$-wave fully charmed tetraquark at electron-ion colliders within the nonrelativistic QCD (NRQCD) factorization framework, at the lowest order in velocity and $\alpha_s$. The value of the NRQCD long-distance matrix element is estimated from two phenomenological potential models. Our studies reveal that the photoproduction of the $1^{+-}$ fully charmed tetraquark may be difficult to observe at HERA and the EicC; nevertheless, its observation prospect at the EIC appears to be bright., Comment: 14 pages, 1 table, 5 figures; updated to match the published version

We propose and demonstrate that the behaviors of long-range, two-site quantum resources can effectively diagnose quantum phases. In an XX spin chain with symmetry-breaking quantum phase transitions, we reveal that the asymptotic and oscillating decay modes of quantum coherence or quantum discord, along with two-site distance, can identify two spin-liquid phases. Furthermore, based on our analytical results of spin correlation functions, we confirm the existence of long-range entanglement in the system and establish a connection between two-site entanglement and quantum phases. Additionally, for the extended Ising model with topological phase transitions, we find that coherence and quantum discord behaviors can also signify topological quantum phases. In particular, we discover the quantum resource freezing phenomenon, where topologically protected long-range quantum resources may have potential applications in quantum information processing., Comment: 4.5 pages, 4 figures plus the supplemental material

In the framework of nonrelativistic QCD (NRQCD) factorization, we compute both the polarized and the unpolarized decay widths for the processes $\eta_b(\chi_{bJ})\to J/\psi J/\psi$, accurate up to next-to-next-to-leading-order (NNLO) in $\alpha_s$. For the first time, we confirm that the NRQCD factorization does hold at NNLO for the process involving triple quarkonia. We find the radiative corrections are considerable. In particular for $\chi_{b2}$, both $\mathcal{O}(\alpha_s)$ and $\mathcal{O}(\alpha_s^2)$ corrections are sizable and negative, and can significantly reduce the leading order prediction. At NNLO, the branching fractions are $8.2\times 10^{-7}$, $6.2\times 10^{-6}$, $7.2\times 10^{-7}$ and $2.7\times 10^{-6}$ for $\eta_b$, $\chi_{b0}$, $\chi_{b1}$ and $\chi_{b2}$ decay, respectively. Our theoretical predictions are consistent with the upper limits measured by the {\tt Belle} Collaboration. Moreover, we investigate the dependence of the theoretical predictions on the ratio of the charm quark mass and the bottom quark mass. By fixing $m_b$ and varying $m_c$ from $1.25$ to $1.9$ GeV, we find the branching fraction can change a factor of $2$, $3$, and $6$ for $\eta_b$, $\chi_{b0}$, and $\chi_{b1}$, respectively. In the phenomenological analysis, with the integrate luminosity $\mathcal{L}=100\,{\rm fb}^{-1}$, we expect about $(5-10)\times 10^3$ $\eta_b(\chi_{bJ})\to J/\psi J/\psi\to \ell \bar{\ell}\ell \bar{\ell}$ events produced at the {\tt LHC}, thus it might be hopeful to search for these processes. On the other hand, there are less than $100$ $\eta_b(\chi_{bJ})\to J/\psi J/\psi$ signal events at the B factory, so it seems the experimental measurements on these channels are quite challenging based on current dataset., Comment: 17 pages, 3 figures, 4 tables; The affiliation and acknowledgement of the first author are updated

As one class of the most important objects in the universe, magnetars can produce a lot of different frequency bursts including X-ray bursts. In \cite{2022ApJS..260...24C}, 75 X-ray bursts produced by magnetar SGR J1935+2154 during an active period in 2020 are published, including the duration and net photon counts of each burst, and waiting time based on the trigger time difference. In this paper, we utilize the power-law model, $dN(x)/dx\propto (x+x_0)^{-\alpha_x}$, to fit the cumulative distributions of these parameters. It can be found that all the cumulative distributions can be well fitted, which can be interpreted by a self-organizing criticality theory. Furthermore, we check whether this phenomenon still exist in different energy bands and find that there is no obvious evolution. These findings further confirm that the X-ray bursts from magnetars are likely to be generated by some self-organizing critical process, which can be explained by a possible magnetic reconnection scenario in magnetars., Comment: 6 pages, 1 figure and 3 tables; published in Research in Astronomy and Astrophysics