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As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively; however, current implementations are limited to basic logical functions such as OR, AND, NOR, and NAND, restricting broader applications. This paper introduces a three-dimensional (3D) coupling model to investigate the counterintuitive phenomena that arise in nonlinear systems under noise. Compared to the one-dimensional Langevin equation and the two-dimensional Duffing equation, the 3D coupling model features more adjustable parameters and coupling interactions, enhancing the system's dynamic behavior. The study demonstrates that increasing noise intensity triggers reverse aperiodic resonance, leading to signal phase reversal and amplitude amplification. This phenomenon is attributed to the motion of Brownian particles in a bistable potential well. Additionally, reverse aperiodic resonance addresses the lack of logical negation in traditional stochastic resonance systems by introducing noise-driven phase reversal, providing a novel alternative to conventional inverters., Comment: 28 pages, 12 figures

Ultra-high frequency linear frequency modulation (UHF-LFM) signal, as a kind of typical non-stationary signal, has been widely used in microwave radar and other fields, with advantages such as long transmission distance, strong anti-interference ability, and wide bandwidth. Utilizing optimal dynamics response has unique advantages in weak feature identification under strong background noise. We propose a new stochastic resonance method in an asymmetric bistable system with the time-varying parameter to handle this special non-stationary signal. Interestingly, the nonlinear response exhibits multiple stochastic resonances (MSR) and inverse stochastic resonances (ISR) under UHF-LFM signal excitation, and some resonance regions may deviate or collapse due to the influence of system asymmetry. In addition, we analyze the responses of each resonance region and the mechanism and evolution law of each resonance region in detail. Finally, we significantly expand the resonance region within the parameter range by optimizing the time scale, which verifies the effectiveness of the proposed time-varying scale method. The mechanism and evolution law of MSR and ISR will provide references for researchers in related fields., Comment: 23 pages, 13 figures

The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative algorithm in order to get the numerical simulations. Here, we investigate the effect of taking the fractional derivative in the dissipative term in function of the parameter a. Our main findings show that the trajectories can remain inside the well or can escape from it depending on a which plays the role of a control parameter. Besides, the parameter a is also relevant for the creation or destruction of chaotic motions. On the other hand, the study of the escape times of the particles from the well, as a result of variations of the initial conditions and the undergoing force F, is reported by the use of visualization techniques such as basins of attraction and bifurcation diagrams, showing a good agreement with previous results. Finally, the study of the escape times versus the fractional parameter a shows an exponential decay which goes to zero when a is larger than one. All the results have been carried out for weak damping where chaotic motions can take place in the non-fractional case and also for a stronger damping (overdamped case), where the influence of the fractional term plays a crucial role to enhance chaotic motions. We expect that these results can be of interest in the field of fractional calculus and its applications.

Over the past two decades, vibrational resonance has garnered significant interest and evolved into a prominent research field. Classical vibrational resonance examines the response of a nonlinear system excited by two signals: a weak, slowly varying characteristic signal, and a fast-varying auxiliary signal. The characteristic signal operates on a much longer time scale than the auxiliary signal. Through the cooperation of the nonlinear system and these two excitations, the faint input can be substantially amplified, showcasing the constructive role of the fast-varying signal. Since its inception, vibrational resonance has been extensively studied across various disciplines, including physics, mathematics, biology, neuroscience, laser science, chemistry, and engineering. Here, we delve into a detailed discussion of vibrational resonance and the most recent advances, beginning with an introduction to characteristic signals commonly used in its study. Furthermore, we compile numerous nonlinear models where vibrational resonance has been observed to enhance readers' understanding and provide a basis for comparison. Subsequently, we present the metrics used to quantify vibrational resonance, as well as offer a theoretical formulation. This encompasses the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, ultrasensitive vibrational resonance, and the role of noise in vibrational resonance. Later, we showcase two practical applications of vibrational resonance: one in image processing and the other in fault diagnosis. This presentation offers a comprehensive and versatile overview of vibrational resonance, exploring various facets and highlighting promising avenues for future research in both theory and engineering applications.

There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around $x_{c}$, the end point of the superconducting dome on the overdoped side, where the cuparte is believed to be well described by the fermi liquid theory. This is the most evident in the observed $\rho_{s}(0)-T_{c}$ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the d-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around $x^{*}$, the so-called pseudogap end point. Through a systematic variational optimization of the disordered 2D $t-J$ model from the resonating valence bond(RVB) perspective, we find that the d-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional d-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the d-wave RVB pairing of the charge neutral spinons becomes essentially immune to the impurity potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at $x^{*}$, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for $x>x^{*}$, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around $x_{c}$., Comment: 12 pages, 8 figures

Understanding the origin of electron incoherence is the first step toward a theoretical description of the non-Fermi liquid behavior of the high-T$_{c}$ cuprate superconductors. Such electron incoherence manifests itself most evidently in the non-Drude behavior of the optical response of the system and the anomalous density fluctuation behavior in the long wave length limit. The spectral weight transfer related to such dissipative response, which is absent in conventional Fermi liquid metal, has direct consequence on the dc transport property of the system in the normal state and the superfluid stiffness in the superconducting state. It is found that such electron incoherence remains significant even in the clean limit and at low temperature and thus must be attributed to the strong electron correlation effect in the cuprate superconductors. Here we study such an intrinsic effect in the 2D $t-J$ model through the variational calculation of its optical conductivity $\sigma(\omega)$. We assume a resonating valence bond ground state as our starting point and find that a significant portion of the total optical spectral weight remains incoherent throughout the phase diagram. The optical absorption is found to extend all the way to an energy of the order of the bare band width. We find that both the total optical weight $\bar{K}$ and the integrated incoherent optical weight $I$ increase monotonically with doping, with their ratio $R_{incoh}=I/\bar{K}$ decreasing monotonically with doping. Our results indicate that the majority part of electron incoherence in the 2D $t-J$ model can be attributed to the electron fractionalization mechanism assumed in such a treatment. We also find that the Drude weight deduced from $D=\bar{K}-I$ scales linearly with hole doping, without any sign of a non-monotonic behavior in the overdoped regime., Comment: 11 pages,8 figures

We have found two kinds of ultra-sensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultra-sensitive vibrational resonance is a transient behavior caused by transient chaos. Considering long-term response, the system will transform from transient chaos to periodic response. The pattern of vibrational resonance will also transform from ultra-sensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultra-sensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultra-sensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from an ultra-sensitive vibrational resonance to a conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultra-sensitive vibrational resonance appears and the plot of the response amplitude versus the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly-periodic, it usually corresponds to the conventional vibrational resonance. The ultra-sensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultra-sensitive vibrational resonance as a transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.

Copper hydroxyhalide materials herbertsmithite ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ and Zn-barlowite ZnCu$_{3}$(OH)$_{6}$FrBr are thought to be the best realizations of the spin-$\frac{1}{2}$ Kagome quantum antiferromagnetic Heisenberg model and are widely believed to host a spin liquid ground state. However, the exact nature of such a novel state of matter is still under strong debate, partly due to the complication related to the occupation disorder between the Zinc and the Copper ions in these systems. In particular, recent nuclear magnetic resonance measurements indicate that the magnetic response of the Kagome plane is significantly spatial inhomogeneous, even though the content of the misplaced Zinc or Copper ions is believed to be very small. Here we use extensive variational optimization to show that the well known $U(1)$-Dirac spin liquid state is extremely sensitive to the introduction of the nonmagnetic Zinc impurity in the Kagome plane. More specifically, we find that the Zinc impurities can significantly reorganize the local spin correlation pattern around them and induce strong spatial oscillation in the magnetic response of the system. We argue that this is a general trend in highly frustrated quantum magnet systems, in which the nonmagnetic impurity may act as strongly relevant perturbation on the emergent resonating valence bond structure in their spin liquid ground state. We also argue that the strong spatial oscillation in the magnetic response should be attributed to the free moment released by the doped Zinc ions and may serve as the smoking gun evidence for the Dirac node in the $U(1)$ Dirac spin liquid state on the Kagome lattice., Comment: 13 pages, 10 figures

It is widely believed that the $U(1)$ spin liquid with a large spinon Fermi surface(SFS state) can be realized in the spin-$\frac{1}{2}$ $J_{1}-J_{4}$ model on the triangular lattice, when the ring exchange coupling $J_{4}$ is sufficiently strong to suppress the 120 degree magnetic ordered state. This belief is supported by many variational studies on this model and seems to be consistent with the observations on the organic spin liquid materials such as $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[Pd(dmit)$_{2}$]$_{2}$, which are systems close to their Mott transition and thus have large $J_{4}$. Here we show through systematic variational search that such a state is never favored in the $J_{1}-J_{4}$ model on the triangular lattice. Instead, a state with broken spatial symmetry is favored in the most probable parameter regime for the SFS state and has an energy much lower than that of the SFS state and other proposed variational states. More specifically, we find that for $J_{4}\ge 0.09J_{1}$, the model favors a valence bond solid state with a $4\times6$ period in its local spin correlation pattern and has a variational energy that is about $5\%$ lower than that of the SFS state. This state is separated from the $\pi$-flux state for $J_{4}\le 0.045J_{1}$ by an intermediate symmetry breaking phase with a zigzag pattern in its local spin correlation. We find that the variational phase diagram we got is in qualitative agreement with that obtained from exact diagonalization on a $6\times6$ cluster., Comment: 17 pages, 18 figures, the spin structure factor of the zigzag phase provided

Designing a real-time framework for the spatio-temporal action detection task is still a challenge. In this paper, we propose a novel real-time action detection framework, YOWOv2. In this new framework, YOWOv2 takes advantage of both the 3D backbone and 2D backbone for accurate action detection. A multi-level detection pipeline is designed to detect action instances of different scales. To achieve this goal, we carefully build a simple and efficient 2D backbone with a feature pyramid network to extract different levels of classification features and regression features. For the 3D backbone, we adopt the existing efficient 3D CNN to save development time. By combining 3D backbones and 2D backbones of different sizes, we design a YOWOv2 family including YOWOv2-Tiny, YOWOv2-Medium, and YOWOv2-Large. We also introduce the popular dynamic label assignment strategy and anchor-free mechanism to make the YOWOv2 consistent with the advanced model architecture design. With our improvement, YOWOv2 is significantly superior to YOWO, and can still keep real-time detection. Without any bells and whistles, YOWOv2 achieves 87.0 % frame mAP and 52.8 % video mAP with over 20 FPS on the UCF101-24. On the AVA, YOWOv2 achieves 21.7 % frame mAP with over 20 FPS. Our code is available on https://github.com/yjh0410/YOWOv2.

In this technical report, we would like to introduce our updates to YOWO, a real-time method for spatio-temporal action detection. We make a bunch of little design changes to make it better. For network structure, we use the same ones of official implemented YOWO, including 3D-ResNext-101 and YOLOv2, but we use a better pretrained weight of our reimplemented YOLOv2, which is better than the official YOLOv2. We also optimize the label assignment used in YOWO. To accurately detection action instances, we deploy GIoU loss for box regression. After our incremental improvement, YOWO achieves 84.9\% frame mAP and 50.5\% video mAP on the UCF101-24, significantly higher than the official YOWO. On the AVA, our optimized YOWO achieves 20.6\% frame mAP with 16 frames, also exceeding the official YOWO. With 32 frames, our YOWO achieves 21.6 frame mAP with 25 FPS on an RTX 3090 GPU. We name the optimized YOWO as YOWO-Plus. Moreover, we replace the 3D-ResNext-101 with the efficient 3D-ShuffleNet-v2 to design a lightweight action detector, YOWO-Nano. YOWO-Nano achieves 81.0 \% frame mAP and 49.7\% video frame mAP with over 90 FPS on the UCF101-24. It also achieves 18.4 \% frame mAP with about 90 FPS on the AVA. As far as we know, YOWO-Nano is the fastest state-of-the-art action detector. Our code is available on https://github.com/yjh0410/PyTorch_YOWO., Comment: 4 pages, 1 figure