Mean‐field treatment (MFT) is frequently applied to approximately predict the dynamics of quantum optics systems. It simplifies the system Hamiltonian by neglecting the quantum statistics of certain ...modes that are driven strongly by lasers or couple weakly with other modes. However, the neglected quantum correlations between different modes result in unanticipated quantum effects and might lead to significantly distinct system dynamics. Here, a general and systematic theoretical framework based on perturbation theory in company with MFT is provided to capture these quantum effects. The form of nonlinear dissipation and parasitic Hamiltonian as well as their relationship to the nonlinear coupling rate are predicted. Furthermore, the indicator is also proposed as a measure of the accuracy of mean‐field treatment. As an example, this theory is applied to quantum frequency conversion, in which mean‐field treatment is commonly applied, to test its limitation under strong pump and large coupling strength. The analytical results show excellent agreement with the numerical simulations. This work clearly reveals the residual quantum effects neglected by MFT and provides a more precise theoretical framework for nonlinear optics and quantum optics.
A general and systematic theoretical framework to reveal the nonlinear dissipations and parasitic interactions neglected by mean‐field approximation in traditional studies of quantum optics systems is developed. The indicator is proposed as a measure of the accuracy of mean‐field treatment. The theory provides an efficient tool to predict the dynamics of nonlinear and quantum optics systems with high precision.
In this study, we investigate the three dimensional J1−J2 model with ferromagnetic interaction using mean field approximation and Monte Carlo techniques. We derive analytical expressions for the ...energy, magnetization, heat capacity, and susceptibility of the model. The Monte Carlo analysis confirms that the mean field approximation predicts the ferromagnetic to paramagnetic phase transition and allows us to estimate the critical temperature and exponents, which satisfy the hyperscaling relation.
•Comprehensive analysis: The research article presents a thorough investigation of the three-dimensional ferromagnetic J1−J2 spin model using both mean field approximation and Monte Carlo techniques.•Analytical insights: Analytical expressions for important thermodynamic quantities using the mean field approximation and numerical validation by Monte Carlo simulations have been done.•Critical temperature and exponents: The study utilizes finite size scaling techniques to estimate the critical temperature and critical exponents of the model at phase transition, which satisfy the hyperscaling relation in three dimensions.•Relevance to condensed matter physics: The research contributes to the field of condensed matter physics, and the findings are expected to be of interest to a wide range of readers in the scientific community.
Large-scale Multi-Agent Reinforcement Learning (MARL) is fundamentally a challenge due to the curse of dimensionality. In a homogeneous multi-agent setting, mean field theory gives an effective way ...of scalable MARL by abstracting other agents to a virtual mean agent, assuming that the influence between agents is equal and infinitesimal. However, in some real scenarios, only several neighboring agents, rather than all agents, affect the decision-making of an agent, and different neighboring agents may have varying degrees of influence on the agent's decision-making. In this paper, not restricted to a homogeneous setting, we propose adaptive mean field MARL, which is based on the attention mechanism and can be used to deal with many-agent scenarios where there may be different influence relationships among agents. Specifically, we first derive the mean field approximation with adaptive weight and give the error bound of the approximation. Then, we propose adaptive mean field Q-Learning and describe how to obtain the adaptive weight. In addition, we discuss the differences between the proposed approach and existing mean-field MARL methods. Finally, we conduct experiments on simulation platforms, and the results show that the performance of the proposed approach outperforms that of the state-of-the-art method.
In hyperdense heterogeneous networks (HetNets), efficient intercell interference management is an important issue. In this paper, using recent advances in mean-field game (MFG) theory, we propose a ...novel game-theoretic approach for interference management in HetNets. The intercell interference management issue in HetNets is formulated as two nested problems: an overlay problem at the macrocell base station (MBS) level and an underlay problem at the small-cell base station (SBS) level. In the overlay problem, the MBS selects the optimal action first, which satisfies its associated users with a minimum amount of cross-layer interference, taking into account the reaction of the SBSs. The underlay problem is then formulated as a noncooperative game among the SBSs. The mean-field theory is exploited to help decouple a complex large-scale optimization problem into a family of localized optimization problems. Thus, each SBS can implement its policy by using only its local information and some macroscopic information. In addition to the achieved tradeoff between spectral efficiency (SE) and energy efficiency (EE), our approach can substantially reduce the communication overhead and convergence time of interference management in hyperdense HetNets. Simulation results are presented to show the effectiveness of the proposed scheme.
Perimeter control is a traffic management approach aimed at regulating vehicular accumulation within urban regional networks by managing flows on all border-crossing roads. Methods based on the ...macroscopic fundamental diagram (MFD) fall short in providing specific metering for individual roads. Recent advancements in the cell transmission model (CTM) have attempted to address this limitation but are hindered by their reliance on centralized control, which requires the availability of full information and authority over traffic generation sites. Our study proposes an innovative decentralized, game-theoretical framework for perimeter control to address these practical challenges. It is structured around two key groups of agents: perimeter agents, tasked with managing border roads, and interior agents, focused on traffic within generation sites. The framework also incorporates mechanisms for interactions between these agents and the road network, aiming to optimize their individual utilities. Additionally, we have developed a multi-agent reinforcement learning (RL) algorithm, extending the mean-field theory concept, to address the complexity of simultaneous learning by multiple agents.
•Developed a perimeter control method for heterogeneous decision-makers.•Applied the macroscopic fundamental diagram concept to simplify perimeter control.•Introduced innovative reinforcement learning techniques for problem-solving.•Demonstrated superior performance using real-world traffic data.
In this paper, we analyze a social imitation model that incorporates internal energy caches (e.g., food/money savings), cost of living, death, and reproduction into the Ultimatum Game. We show that ...when imitation (and death) occurs, a natural correlation between selfishness and cost of living emerges. However, in all societies that do not collapse, non-Nash sharing strategies emerge as the de facto result of imitation. We explain these results by constructing a mean-field approximation of the internal energy cache informed by time-varying distributions extracted from experimental data.
•In this paper, we analyze a social imitation model of the Ultimatum Game.•We show a a natural correlation between selfishness and cost of living emerges.•We explain these results by constructing a mean-field approximation.
Finding the optimal signal timing strategy is a difficult task for the problem of large-scale traffic signal control (TSC). Multiagent reinforcement learning (MARL) is a promising method to solve ...this problem. However, there is still room for improvement in extending to large-scale problems and modeling the behaviors of other agents for each individual agent. In this article, a new MARL, called cooperative double <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-learning (Co-DQL), is proposed, which has several prominent features. It uses a highly scalable independent double <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-learning method based on double estimators and the upper confidence bound (UCB) policy, which can eliminate the over-estimation problem existing in traditional independent <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-learning while ensuring exploration. It uses mean-field approximation to model the interaction among agents, thereby making agents learn a better cooperative strategy. In order to improve the stability and robustness of the learning process, we introduce a new reward allocation mechanism and a local state sharing method. In addition, we analyze the convergence properties of the proposed algorithm. Co-DQL is applied to TSC and tested on various traffic flow scenarios of TSC simulators. The results show that Co-DQL outperforms the state-of-the-art decentralized MARL algorithms in terms of multiple traffic metrics.
•A continuous CRF graph convolution (CRFConv) is proposed to model the upsampling process of point cloud features.•A point cloud segmentation network based on the CRFConv is built to enhance the ...location ability of the network.•The classical discrete CRF is also reformulated as an additional graph convolution to refine the labels.•A dual CRF network is implemented to model the data affinity in both feature space and label space simultaneously.•The experiments on various challenging benchmarks demonstrate the effectiveness and robustness of the proposed method.
Point cloud segmentation is the foundation of 3D environmental perception for modern intelligent systems. To solve this problem and image segmentation, conditional random fields (CRFs) are usually formulated as discrete models in label space to encourage label consistency, which is actually a kind of postprocessing. In this paper, we reconsider the CRF in feature space for point cloud segmentation because it can capture the structure of features well to improve the representation ability of features rather than simply smoothing. Therefore, we first model the point cloud features with a continuous quadratic energy model and formulate its solution process as a message-passing graph convolution, by which it can be easily integrated into a deep network. We theoretically demonstrate that the message passing in the graph convolution is equivalent to the mean-field approximation of a continuous CRF model. Furthermore, we build an encoder-decoder network based on the proposed continuous CRF graph convolution (CRFConv), in which the CRFConv embedded in the decoding layers can restore the details of high-level features that were lost in the encoding stage to enhance the location ability of the network, thereby benefiting segmentation. Analogous to the CRFConv, we show that the classical discrete CRF can also work collaboratively with the proposed network via another graph convolution to further improve the segmentation results. Experiments on various point cloud benchmarks demonstrate the effectiveness and robustness of the proposed method. Compared with the state-of-the-art methods, the proposed method can also achieve competitive segmentation performance.
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