Search

Gamma-ray bursts (GRBs), both from merger of binary compact objects (short GRBs) and collapse of massive stars (long GRBs), are expected to occur in the dense environments, e.g., the accretion disk of active galactic nuclei (AGN). The propagating of GRB jets in such dense environment will result in multiband transients. Investigating the properties of these transients plays important roles in their identification, understanding the jet structure and constraining population of the star and compact object in AGN disks. In this work, we intend to study the propagation and emission of a two-component GRB jet (a fast narrow component and wide slow one) in the AGN disk. We consider the influence of wind from the short and long GRB progenitors, which would reconstruct the surrounding density distribution and form a cavity in the AGN disk. We find that the long GRB jets will be chocked, the dynamcis and the emission are resemble to the case without cavity. The narrow and wide cocoon breakout emission can be detected by EP and HXMT, respectively. For short GRBs, we expect a non-thermal afterglow emission from the wide jet and a cocoon breakout emission from the chocked narrow jet, which can be monitored by EP and HXMT, respectively. Therefore, the joint observations by EP and HXMT might be helpful to distinguish the type of GRBs in the AGN disk and the jet components., Comment: 15 pages, 6 figures, 1 table

Numerous studies have demonstrated the manifold benefits of tennis, such as increasing overall physical and mental health. Unfortunately, many children and youth from low-income families are unable to engage in this sport mainly due to financial constraints such as private lesson expenses as well as logistical concerns to and back from such lessons and clinics. While several tennis self-training systems exist, they are often tailored for professionals and are prohibitively expensive. The present study aims to classify tennis players' skill levels and classify tennis strokes into phases characterized by motion attributes for a future development of an AI-based tennis self-training model for affordable and convenient applications running on devices used in daily life such as an iPhone or an Apple Watch for tennis skill improvement. We collected motion data, including Motion Yaw, Roll and Pitch from inertial measurement units (IMUs) worn by participating junior tennis players. For this pilot study, data from twelve participants were processed using Support Vector Machine (SVM) algorithms. The SVM models demonstrated an overall accuracy of 77% in classifying players as beginners or intermediates, with low rates of false positives and false negatives, effectively distinguishing skill levels. Additionally, the tennis swings were successfully classified into five phases based on the collected motion data. These findings indicate that SVM-based classification can be a reliable foundation for developing an equitable and accessible AI-driven tennis training system., Comment: 21 pages, 9 figures, 1 table

We present the discovery and early observations of the nearby Type II supernova (SN) 2024ggi in NGC 3621 at 6.64 +/- 0.3 Mpc. The SN was caught 5.8 (+1.9 -2.9) hours after its explosion by the ATLAS survey. Early-phase, high-cadence, and multi-band photometric follow-up was performed by the Kinder (Kilonova Finder) project, collecting over 1000 photometric data points within a week. The combined o- and r-band light curves show a rapid rise of 3.3 magnitudes in 13.7 hours, much faster than SN 2023ixf (another recent, nearby, and well-observed SN II). Between 13.8 and 18.8 hours after explosion SN 2024ggi became bluer, with u-g colour dropping from 0.53 to 0.15 mag. The rapid blueward evolution indicates a wind shock breakout (SBO) scenario. No hour-long brightening expected for the SBO from a bare stellar surface was detected during our observations. The classification spectrum, taken 17 hours after the SN explosion, shows flash features of high-ionization species such as Balmer lines, He I, C III, and N III. Detailed light curve modeling reveals critical insights into the properties of the circumstellar material (CSM). Our favoured model has an explosion energy of 2 x 10^51 erg, a mass-loss rate of 10^-3 solar_mass/yr (with an assumed 10 km/s wind), and a confined CSM radius of 6 x 10^14 cm. The corresponding CSM mass is 0.4 solar_mass. Comparisons with SN 2023ixf highlight that SN 2024ggi has a smaller CSM density, resulting in a faster rise and fainter UV flux. The extensive dataset and the involvement of citizen astronomers underscore that a collaborative network is essential for SBO searches, leading to more precise and comprehensive SN characterizations., Comment: 11 pages, 5 figures in manuscript, 6 pages in appendix, submitted to ApJL

Obstructed atomic insulator is recently proposed as an unconventional material, in which electric charge centers localized at sites away from the atoms. A half-filling surface state would emerge at specific interfaces cutting through these charge centers and avoid intersecting any atoms. In this article, we utilized angle-resolved photoemission spectroscopy and density functional theory calculations to study one of the obstructed atomic insulator candidates, NiP$_2$. A floating surface state with large effective mass that is isolated from all bulk states is resolved on the (100) cleavage plane, distinct from previously reported surface states in obstructed atomic insulators that are merged into bulk bands. Density functional theory calculation results elucidate that this floating surface state is originated from the obstructed Wannier charge centers, albeit underwent surface reconstruction that splits the half-filled obstructed surface state. Our findings not only shed lights on the spectroscopy study of obstructed atomic insulators and obstructed surface states, but also provide possible route for development of new catalysts., Comment: 21 pages, 5 figures

In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from simple qubit arrays, specifically grid lattices. The first approach utilizes a subset of qubits as tunable couplers, effectively yielding a range of non-trivial graph-based Hamiltonians. The second approach employs dynamic graph engineering by periodically activating and deactivating couplers, enabling the creation of effective quantum walks with longer-range couplings. Numerical simulations verify the effective dynamics of these approaches. In terms of these two approaches, we explore implementing various graphs, including cubes and fullerenes, etc, on two-dimensional lattices. These techniques facilitate the realization of analog quantum simulation, particularly continuous-time quantum walks discussed in detail in this manuscript, for different computational tasks on superconducting quantum chips despite their inherent low dimensional simple architecture., Comment: 9 pages, 12 figures

Recently, unconventional antiferromagnets that enable the splitting of electronic spins have been theoretically proposed and experimentally realized, where the magnetic sublattices containing moments pointing at different directions are connected by a novel set of symmetries. Such spin splitting (SS) is substantial, $k$-dependent, and independent of the spin-orbit coupling strength, making these magnets promising materials for antiferromagnetic spintronics. Here, combined with angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we perform a systematic study on CrSb, a metallic spin-split antiferromagnet candidate with $T_N$ = 703 K. Our data reveals the electronic structure of CrSb along both out-of-plane and in-plane momentum directions, which renders anisotropic $k$-dependent SS and agrees well with the calculational results. The magnitude of such SS reaches up to at least 0.8 eV at non-high-symmetry momentum points, which is significantly higher than the largest known SOC-induced SS. This compound expands the choice of materials in the field of antiferromagnetic spintronics and is likely to stimulate subsequent investigations of high-efficiency spintronic devices that are functional at room temperature., Comment: 14 pages, 4 figures

This paper extends the work of Arcidiacono and Miller (2011, 2019) by introducing a novel characterization of finite dependence within dynamic discrete choice models, demonstrating that numerous models display 2-period finite dependence. We recast finite dependence as a problem of sequentially searching for weights and introduce a computationally efficient method for determining these weights by utilizing the Kronecker product structure embedded in state transitions. With the estimated weights, we develop a computationally attractive Conditional Choice Probability estimator with 2-period finite dependence. The computational efficacy of our proposed estimator is demonstrated through Monte Carlo simulations.

Recently, much attention has been focused on the false vacuum islands that are flooded by an expanding ocean of true-vacuum bubbles slightly later than most of the other parts of the world. These delayed decay regions will accumulate locally larger vacuum energy density by staying in the false vacuum longer than those already transited into the true vacuum. A false vacuum island with thus acquired density contrast of a super-horizon size will evolve locally from radiation dominance to vacuum dominance, creating a local baby Universe that can be regarded effectively as a local closed Universe. If such density contrasts of super-horizon sizes can ever grow large enough to exceed the threshold of gravitational collapse, primordial black holes will form similar to those collapsing curvature perturbations on super-horizon scales induced by small-scale enhancements during inflation. If not, such density contrasts can still induce curvature perturbations potentially observable today. In this paper, we revisit and elaborate on the generations of primordial black holes and curvature perturbations from delayed-decayed false vacuum islands during asynchronous first-order phase transitions with fitting formulas convenient for future model-independent studies., Comment: v1, two columns, 16 pages, 8 figures; v2, 17 pages, 8 figures, minor revision, version accepted for publication in Sci. China Phys. Mech. Astron. (SCPMA); v3, to match the published version

The effective central charge (denoted by $c_{\text{eff}}$) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient $c_{LR}$ of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this article, we propose the inequalities, $0 \leq c_{LR} \leq c_{\text{eff}} \leq \min (c_L,c_R)$. They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them., Comment: 4 pages, 1 figure + 4 pages, few comments added

In this study, we introduce the DriveEnv-NeRF framework, which leverages Neural Radiance Fields (NeRF) to enable the validation and faithful forecasting of the efficacy of autonomous driving agents in a targeted real-world scene. Standard simulator-based rendering often fails to accurately reflect real-world performance due to the sim-to-real gap, which represents the disparity between virtual simulations and real-world conditions. To mitigate this gap, we propose a workflow for building a high-fidelity simulation environment of the targeted real-world scene using NeRF. This approach is capable of rendering realistic images from novel viewpoints and constructing 3D meshes for emulating collisions. The validation of these capabilities through the comparison of success rates in both simulated and real environments demonstrates the benefits of using DriveEnv-NeRF as a real-world performance indicator. Furthermore, the DriveEnv-NeRF framework can serve as a training environment for autonomous driving agents under various lighting conditions. This approach enhances the robustness of the agents and reduces performance degradation when deployed to the target real scene, compared to agents fully trained using the standard simulator rendering pipeline., Comment: Project page: https://github.com/muyishen2040/DriveEnvNeRF

The nearby long-duration GRB 191019A recently detected by Swift lacks an associated supernova and belongs to a host galaxy with little star formation activity, suggesting that the origin of this burst is the result of a merger of two compact objects with dynamical interactions in a high-density medium of an active galactic nucleus. Given the potential motivation of this event, and given that it occurs in such a high-density environment, the ejecta-circumstellar medium (CSM) interaction cannot be ignored as possibly contributing to the kilonova emission. Here, we theoretically calculate the kilonova emission by considering the contribution of the ejecta-CSM interaction in a high-density environment. We find that the contribution to the kilonova emission from the ejecta-CSM interaction will dominate at a later time, and a smaller ejecta mass will have a stronger kilonova emission from the ejecta-CSM interaction. Moreover, we try to apply it to GRB 191019A, but we find that it is difficult to identify the possible kilonova emission from the observations, due to the contribution of the bright host galaxy. On the other hand, less injected mass (less than $M_{\rm ej}=2\times10^{-5}M_{\odot}$) will be required if one can detect the kilonova emission associated with a GRB 191019A-like event in the future. The {\em r}-process-powered and spin energy contributions from the magnetar are also discussed., Comment: 10 pages, 6 figures, updated the rederence list. ApJ in press, and matched with the published verison

Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems., Comment: 37 pages, 1 figure

Static analysis, the process of examining code without executing it, is crucial for identifying software issues. Yet, static analysis is hampered by its complexity and the need for customization for different targets. Traditional static analysis tools require extensive human effort and are often limited to specific target programs and programming languages. Recent advancements in Large Language Models (LLMs), such as GPT-4 and Llama, offer new capabilities for software engineering tasks. However, their application in static analysis, especially in understanding complex code structures, remains under-explored. This paper introduces a novel approach named E&V , which leverages LLMs to perform static analysis. Specifically, E&V employs LLMs to simulate the execution of pseudo-code, effectively conducting static analysis encoded in the pseudo-code with minimal human effort, thereby improving the accuracy of results. E&V includes a verification process for pseudo-code execution without needing an external oracle. This process allows E&V to mitigate hallucinations of LLMs and enhance the accuracy of static analysis results. We have implemented E&V in a prototype tool designed for triaging crashes through backward taint analysis. This prototype, paired with GPT-4-32k, has been applied to triage 170 recently fixed Linux kernel bugs across seven bug categories. Our experiments demonstrate that the prototype correctly identifies the blamed function in 81.2% of the cases. Additionally, we observe that our novel verification process significantly improves the accuracy, increasing it from 28.2% to 81.2%., Comment: 10 pages, under submission

The strongly coupled system like the quark-hadron transition (if it is of first order) is becoming an active play yard for the physics of cosmological first-order phase transitions. However, the traditional field theoretic approach to strongly coupled first-order phase transitions is of great challenge, driving recent efforts from holographic dual theories with explicit numerical simulations. These holographic numerical simulations have revealed an intriguing linear correlation between the phase pressure difference (pressure difference away from the wall) to the nonrelativistic terminal velocity of an expanding planar wall, which has been reproduced analytically alongside both cylindrical and spherical walls from perfect-fluid hydrodynamics in our previous study but only for a bag equation of state. We also found, in our previous study, a universal quadratic correlation between the wall pressure difference (pressure difference near the bubble wall) to the nonrelativistic terminal wall velocity regardless of wall geometries. In this paper, we will generalize these analytic relations between the phase/wall pressure difference and terminal wall velocity into a more realistic equation of state beyond the simple bag model, providing the most general predictions so far for future tests from holographic numerical simulations of strongly coupled first-order phase transitions, Comment: v1, 22 pages, 10 figures; v2, two columns, 16 pages, 8 figures, extended discussion on the difference between phase pressure difference and wall pressure difference, version accepted for publication in Physical Review D; v3, to match the published version

People with blindness and low vision (pBLV) encounter substantial challenges when it comes to comprehensive scene recognition and precise object identification in unfamiliar environments. Additionally, due to the vision loss, pBLV have difficulty in accessing and identifying potential tripping hazards on their own. In this paper, we present a pioneering approach that leverages a large vision-language model to enhance visual perception for pBLV, offering detailed and comprehensive descriptions of the surrounding environments and providing warnings about the potential risks. Our method begins by leveraging a large image tagging model (i.e., Recognize Anything (RAM)) to identify all common objects present in the captured images. The recognition results and user query are then integrated into a prompt, tailored specifically for pBLV using prompt engineering. By combining the prompt and input image, a large vision-language model (i.e., InstructBLIP) generates detailed and comprehensive descriptions of the environment and identifies potential risks in the environment by analyzing the environmental objects and scenes, relevant to the prompt. We evaluate our approach through experiments conducted on both indoor and outdoor datasets. Our results demonstrate that our method is able to recognize objects accurately and provide insightful descriptions and analysis of the environment for pBLV.

In this letter, we show the Unruh temperature of the photon sphere for an AdS$_4$-Schwarzschild black hole can be determined holographically from the retarded Green's function and is proportional to its circumference according to a boundary observer. We then sharpen the conjecture that the photon sphere, as seen by a boundary observer, is the spatial Fourier transform of the response function. The conjecture is found to be in excellent agreement with our numerics after certain long-lived excitations -- associated with geodesics traveling between boundary points -- are removed from the response, which is then controlled by the short-lived excitations of the AdS black hole., Comment: 6 pages, 5 figures. Simplified Abstract. Correction added to Equation 20. Included additional citations. Corrected a dotted line in Figure 2. The definition of the impact parameter is now self-consistent in Figure 4. Larger labels in Figure 5

The gravitational-wave energy-density spectra from cosmological first-order phase transitions crucially depend on the terminal wall velocity of asymptotic bubble expansion when the driving force from the effective potential difference is gradually balanced by the backreaction force from the thermal plasma. Much attention has previously focused on the backreaction force acting on the bubble wall alone but overlooked the backreaction forces on the sound shell and shock-wave front, if any, which have been both numerically and analytically accomplished in our previous studies but only for a bag equation of state. In this paper, we will generalize the backreaction force on bubble expansion beyond the simple bag model., Comment: 18 pages, 1 figure, two columns, to match the published version in Physical Review D

Random packings of stiff rods are self-supporting mechanical structures stabilized by their geometrical and topological complexity. To understand why, we deploy X-ray computerized tomography to unveil the structure of the packing. This allows us to define and directly visualize the spatial variations in "entanglement," a mesoscopic field that characterizes the local average crossing number, a measure of the topological complexity of the packing. We show that the entanglement field has information that is distinct from the density, orientational order, and contact distribution of the packing. We find that increasing the aspect ratio of the constituent rods in a packing leads to an abrupt change in the entanglement, correlated with a sharp transition in the mechanical response of the packing. This leads to an entanglement phase diagram for the mechanical response of dense rod packings that is likely relevant for a broad range of problems that goes beyond our specific study.

Black hole-neutron star (BH-NS) mergers are expected to emit gravitational-wave (GW) and electromagnetic (EM) counterparts when the NS is tidally disrupted or plunges into the BH. Recently, GW 200105 and GW200115 were claimed as originating in BH-NS mergers, even GW 200105 remains in debate. Several optical source candidates are reported to possible associate with the two GW events, but not confirmed yet. In this work, we assume that the BH is charged (the NS is naturally charged) and try to constrain the charge of the BH by using the possible associated EM emission from the charged BH and NS system working in the inspiral regime. We adopt electric and magnetic dipole radiations for the binaries which power a Poynting-flux-dominated outflow to accelerate electrons. Then, it produces the observed EM radiation via synchrotron radiation. We find that the conversion efficiency in the X-ray band is much higher than that of the ultraviolet (UV), near-infrared, and radio bands. The estimated maximum charge-to-mass ratio (the charge for unit mass) of the BH is $1.12\times 10^{-6}$ and $1.53\times 10^{-6}$ esu for the binary systems of GW200105 and GW200115, respectively, if magnetic field strength $B_{p}\lesssim ~10^{16}$ G and period $P>~1$ ms for the NS spin., Comment: 13 pages, 4 Tables, and 2 Figures. Accepted for publication in PRD

We present the photometric and spectroscopic evolution of SN 2022oqm, a nearby multi-peaked hydrogen- and helium-weak calcium-rich transient (CaRT). SN 2022oqm was detected 13.1 kpc from its host galaxy, the face-on spiral galaxy NGC 5875. Extensive spectroscopic coverage reveals an early hot (T >= 40,000 K) continuum and carbon features observed $\sim$1~day after discovery, SN Ic-like photospheric-phase spectra, and strong forbidden calcium emission starting 38 days after discovery. SN 2022oqm has a relatively high peak luminosity (MB = -17 mag) for (CaRTs), making it an outlier in the population. We determine that three power sources are necessary to explain the light curve (LC), with each corresponding to a distinct peak. The first peak is powered by an expanding blackbody with a power law luminosity, suggesting shock cooling by circumstellar material (CSM). Subsequent LC evolution is powered by a double radioactive decay model, consistent with two sources of photons diffusing through optically thick ejecta. From the LC, we derive an ejecta mass and 56Ni mass of ~0.6 solar masses and ~0.09 solar masses. Spectroscopic modeling suggests 0.6 solar masses of ejecta, and with well-mixed Fe-peak elements throughout. We discuss several physical origins for SN 2022oqm and find either a surprisingly massive white dwarf progenitor or a peculiar stripped envelope model could explain SN 2022oqm. A stripped envelope explosion inside a dense, hydrogen- and helium-poor CSM, akin to SNe Icn, but with a large 56Ni mass and small CSM mass could explain SN 2022oqm. Alternatively, helium detonation on an unexpectedly massive white dwarf could also explain SN 2022oqm., Comment: 35 pages, 17 figures, 7 tables, Accepted for Publication in ApJ

When an interface connects two CFTs, the entanglement entropy between the two CFTs is determined by a quantity called the effective central charge. The effective central charge does not have a simple form in terms of the central charges of the two CFTs, but intricately depends on the transmissive properties of the interface. In this article, we examine universal properties of the effective central charge. We first clarify how the effective central charge appears when considering general subsystems of the interface CFT. Then using this result and ideas used in the proof of the $c$-theorem, we provide a universal upper bound on the effective central charge. In past studies, the effective central charge was defined only in two dimensions. We propose an analogue of the effective central charge in general dimensions possessing similar universal properties as in two dimensions., Comment: 25 pages, 10 figures, revising an error in Section 3.3 and adding some explanations in Section 3.1

Static analysis is a widely used technique in software engineering for identifying and mitigating bugs. However, a significant hurdle lies in achieving a delicate balance between precision and scalability. Large Language Models (LLMs) offer a promising alternative, as recent advances demonstrate remarkable capabilities in comprehending, generating, and even debugging code. Yet, the logic of bugs can be complex and require sophisticated reasoning and a large analysis scope spanning multiple functions. Therefore, at this point, LLMs are better used in an assistive role to complement static analysis. In this paper, we take a deep dive into the open space of LLM-assisted static analysis, using use-before-initialization (UBI) bugs as a case study. To this end, we develop LLift, a fully automated framework that interfaces with both a static analysis tool and an LLM. By carefully designing the framework and the prompts, we are able to overcome a number of challenges, including bug-specific modeling, the large problem scope, the non-deterministic nature of LLMs, etc. Tested in a real-world scenario analyzing nearly a thousand potential UBI bugs produced by static analysis, LLift demonstrates a potent capability, showcasing a reasonable precision (50%) and appearing to have no missing bugs. It even identified 13 previously unknown UBI bugs in the Linux kernel. This research paves the way for new opportunities and methodologies in using LLMs for bug discovery in extensive, real-world datasets.

Revisiting the Coon amplitude, a deformation of the Veneziano amplitude with a logarithmic generalization of linear Regge trajectories, we scrutinize its potential origins in a worldsheet theory by proposing a definition of its $q$-deformation through the integral representation of the $q$-beta function. By utilizing $q$-deformed commutation relations and vertex operators, we derive the Coon amplitude within the framework of the dual resonance model. We extend this to the open-string context by $q$-deforming the Lie algebra $\mathfrak{su}(1,1)$, resulting in a well-defined $q$-deformed open superstring amplitude. We further demonstrate that the $q$-prefactor in the Coon amplitude arises naturally from the property of the $q$-integral. Furthermore, we find that two different types of $q$-prefactors, corresponding to different representations of the same scattering amplitude, are essentially the same by leveraging the properties of $q$-numbers. Our findings indicate that the $q$-deformed string amplitude defines a continuous family of amplitudes, illustrating how string amplitudes with a finite $\alpha^\prime$ uniquely flow to the amplitudes of scalar scattering in field theory at energy scale $\Lambda$ as $q$ changes from $1$ to $0$. This happens without the requirement of an $\alpha^\prime$ expansion, presenting a fresh perspective on the connection between string and field theories.

Small Object Detection (SOD) is an important machine vision topic because (i) a variety of real-world applications require object detection for distant objects and (ii) SOD is a challenging task due to the noisy, blurred, and less-informative image appearances of small objects. This paper proposes a new SOD dataset consisting of 39,070 images including 137,121 bird instances, which is called the Small Object Detection for Spotting Birds (SOD4SB) dataset. The detail of the challenge with the SOD4SB dataset is introduced in this paper. In total, 223 participants joined this challenge. This paper briefly introduces the award-winning methods. The dataset, the baseline code, and the website for evaluation on the public testset are publicly available., Comment: This paper is included in the proceedings of the 18th International Conference on Machine Vision Applications (MVA2023). It will be officially published at a later date. Project page : https://www.mva-org.jp/mva2023/challenge

Entangled qudits, the high-dimensional entangled states, play an important role in the study of quantum information. How to prepare entangled qudits in an efficient and easy-to-operate manner is still a challenge in quantum technology. Here, we demonstrate a method to engineer frequency entangled qudits in a spontaneous parametric downconversion process. The proposal employs an angle-dependent phase-matching condition in a nonlinear crystal, which forms a classical-quantum mapping between the spatial (pump) and spectral (biphotons) degrees of freedom. In particular, the pump profile is separated into several bins in the spatial domain, and thus shapes the down-converted biphotons into discrete frequency modes in the joint spectral space. Our approach provides a feasible and efficient method to prepare a high-dimensional frequency entangled state. As an experimental demonstration, we generate a three-dimensional entangled state by using a homemade variable slit mask., Comment: 9 pages, 9 figures

The AdS/CFT correspondence connects bulk fields $\phi$ to boundary operators $\mathcal{O}$ characterized by source frequency $\omega$ and angular momentum $l$. Here we explore their connection to massless particles with an impact parameter $b=\omega/l$. In the AdS Schwarzschild spacetime, these particles follow unstable orbits around the photon sphere -- with Lyapunov exponent $\lambda$ -- when $b$ is near a critical value. The behavior of the bulk field is obtained numerically and then studied using an analytic approach, which leads to a precise approximate formula for the amplitude of the bulk field $\phi$. This gives the correct qualitative behavior for the system, with the amplitude of the field taking the shape of an arrowhead in tortoise coordinates. The field behaves analogously to the massless particles, and the amplitude of $\phi$ diverges at the critical impact parameter when the source frequency takes the value $\omega \approx \lambda l$, where $\lambda$ is the Lyapunov exponent of the null geodesics. We find this transition occurs when $b = \lambda$. We show this is precisely when the first QNM becomes available, and obtain an approximate formula for the first few overtones., Comment: 33 pages, 7 figures. v2. Amplification formula corrected. Improved discussion of numerics. Added additional citations. Additional context added for QNM argument. Abstract updated

For one-dimension Brownian motion in the confined system with the size $L$, the mean-squared displacement(MSD) defined by $\left \langle (x-x_0)^2 \right\rangle$ should be proportional to $t^{\alpha(t)}$. The power $\alpha(t)$ should range from $1$ to $0$ over time, and the MSD turns from $2Dt$ to $c L^2$, here the coefficient $c$ independent of $t$, $D$ being the diffusion coefficient. The paper aims to quantitatively solve the MSD in the intermediate confinement regime. The key to this problem is how to deal with the propagator and the normalization factor of the Fokker-Planck equation(FPE) with the Dirichlet Boundaries. Applying the Euler-Maclaurin approximation(EMA) and integration by parts for the small $t$, we obtain the MSD being $2Dt(1-\frac{2\sqrt{\xi} }{3\pi\sqrt{\pi}})$, with $t_{ch}=\frac{L^2}{4\pi^2D},\xi\equiv \frac{t}{t_{ch}}$, and the power $\alpha(t)$ being $\frac{1-0.18\sqrt{\xi}}{1-0.12\sqrt{\xi}}$. Further, we analysis the MSD and the power for the $d$-dimension system with $\gamma$-dimension confinement. In the case of $\gamma< d$, there exists the sub-diffusive behavior in the intermediate time. The universal description is consistent with the recent experiments and simulations in the micro-nano systems. Finally, we calculate the position variance(PV) meaning $\left\langle (x-\left\langle x \right\rangle)^2 \right\rangle$. Under the initial condition referring to the different probability density function(PDF) being $p_{0}(x)$, MSD and PV should exhibit different dependencies on time, which reflect corresponding diffusion behaviors.As examples, the paper discusses the representative initial PDFs reading $p_{0}(x)=\delta(x-x_0)$, with the midpoint $x_0=\frac{L}{2}$ and the endpoint $x_0=\epsilon$(or $0^+$).The MSD(equal to PV) reads $2Dt(1-\frac{5\pi^3 Dt}{L^2})$,and $\frac{4}{\pi}(2Dt)[1+\frac{2\sqrt{\pi Dt}}{L}]$for the small $t$,respectively., Comment: 18 pages, 4 figurea