Self-consistent mean field approximation and application in three-flavor NJL model

In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces a new parameter,α,that cannot be fixed in advance by the mean field approach itself.Due to the lack of experimental data,the parameter,α,is undetermined.Hence,it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation.αaffects numerous properties of the chiral phase transitions,such as the position of the phase transition point and the order of phase transition.Additionally,increasingαwill decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero.Finally,we observed thatαaffects the equation of state(EOS)of the quark matter,and the sound velocity can be calculated to determine the stiffness of the EOS,which provides a good basis for studying the neutron star mass-radius relationship.

Novel self-consistent mean field approximation and its application in strong interaction phase transitions

We propose a novel self-consistent mean field approximation method by means of a Fierz transformation,taking the Nambu-Jona-Lasinio model as an example.This new self-consistent mean field approximation introduces a new free parameter a to be determined experimentally.When a assumes the value of 0.5,the approximation reduces to the mean field calculation commonly used in the past.Subsequently,we study the influence of the undetermined parameter a on the phase diagram of the two-flavor strong interaction matter.The value of a plays a crucial role in the strong interaction phase diagram,as it not only changes the position of the phase transition point of strong interaction matter,but also affects the order of the phase transition.For example,when a is greater than the critical valueαc = 0.71,then the strong interaction matter phase diagram no longer has a critical end point.In addition,in the case of zero temperature and finite density,we found that when a>1.044,the pseudo-critical chemical potential corresponds to ～4-5 times the saturation density of the nuclear matter,which agrees with the expected results from the picture of the hadrons degree of freedom.The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.

Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

A combination of the iterative perturbation theory （ITP） of the dynamical mean field theory （DMFT） and coherentpotential approximation （CPA） is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix tij^mn（m ≠ n） are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.

Plasma Simulation beyond Rigid-Macroparticle Approximation

Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocities, into a macroparticle, and do a global motion. This is a distorted picture because what each macroparticle do is to break into, because of differences among velocities of contained realistic particles, pieces with different destinations at next time point, rather than a global moving to a destination at next time point. Therefore, the scientific validity of results obtained from such an approximation cannot be warranted. Here, we propose a solution to this problem. It can fundamentally warrant exact solutions of plasma self-consistent fields and hence those of microscopic distribution function.

MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R^2

Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.

银行货币储备博弈的强化学习方法

在大规模银行交互系统中,各银行可通过控制与中央银行的借贷率来使自身对数货币储备尽可能地接近样本均值,从而降低系统性风险发生的概率.然而当状态过程与目标函数的参数未知时,无法直接求解随机微分博弈问题得到纳什均衡.本文结合平均场博弈理论与连续时间强化学习的相关方法,构造了一组大规模银行借贷网络中的近似纳什均衡.首先通过求解向前向后耦合HJB-FPK方程,得到代表银行的平均场均衡策略;再通过所得策略的形式,设计出迭代参数的方法用以刻画参数未知时的近似最优策略;最后通过学到的参数,构造银行数量较大时的近似纳什均衡.

Quantum Field Theory of Graphene with Dynamical Partial Symmetry Breaking

The quantum field theory approach has been proposed for the description of graphene electronic properties. It generalizes massless Dirac fermion model and is based on the Dirac-Hartree-Fock self-consistent field approximation and assumption on antiferromagnetic ordering of graphene lattice. The developed approach allows asymmetric charged carriers in single layer graphene with partially degenerated Dirac cones.

Mean field game of optimal relative investment with jump risk

In this paper,we study the n-player game and the mean field game under the constant relative risk aversion relative performance on terminal wealth,in which the interaction occurs by peer competition.In the model with n agents,the price dynamics of underlying risky assets depend on a common noise and contagious jump risk modeled by a multi-dimensional nonlinear Hawkes process.With a continuum of agents,we formulate the mean field game problem and characterize a deterministic mean field equilibrium in an analytical form under some conditions,allowing us to investigate some impacts of model parameters in the limiting model and discuss some financial implications.Moreover,based on the mean field equilibrium,we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large.The explicit order of the approximation error is also derived.

一维Sznajd舆论模型相变的研究

略去一维标准Szna jd舆论模型的第二个规则,修改后的模型演化的决定时间分布没有发生变化,但弛豫时间延长了;反铁磁性吸引子消失了,铁磁性终态吸引子出现的概率对初始态度人员密度有着重要的依赖关系.进一步在平均场的近似下,修改后的一维Szna jd舆论模型存在相变.

一种基于多尺度MRF模型的边缘检测算法

边缘检测中通常要处理两个问题：在单一尺度上检测和定位之间存在的矛盾；不同尺度上的边缘集成．采用多尺度ＭＲＦ模型是有效的途径之一，该模型引入线过程，用以表示边缘的确切位置，同时又能用任意适当的函数集成不同尺度上的边缘．本文根据ＧＢＦ不等式近似计算均值场，导出一组关于均值场的确定算式，显式地表示边缘间的相互作用以及模型参数对检测结果的影响，与文献［１］相比，需要较少的计算时间，并给出了用该算法处理几幅实际图像的实验结果．

生境破坏的空间结构对集合种群续存的影响(英文)

生境破坏及其影响是生态学亟待解决的问题之一.目前的研究主要集中在破坏数量,即遭破坏生境的比例,对物种续存的影响方面;其中最主要的结论是Levins原理和适合生境斑块最小数量(MASH),而关于生境破坏的空间结构的研究却比较稀少.在本文中,我们首先将偶对近似引入到集合种群的研究当中,并替代原有的均匀场假设.然后我们对生境破坏导致的集合种群大小、空间结构以及分布等做了全面讨论.结果显示:随破坏比例的增加,集合种群大小将下降并且其分布将远离破坏生境,进一步聚集式分布结构将瓦解.随着破坏规则化的下降,集合种群将萎缩并使其聚集结构崩溃,在破坏生境周围集合种群起初将增加然后迅速消失.根据这些结果,我们可以对边界效应进行分析:不能用破坏比例描述生境破坏的程度和影响,而只能用破坏区域边界的长短来描述.根据边界效应,我们可以得出在一连通生境上物种保护的条件是生境破坏后剩余的适合生境比例应该大于破坏前原始生境的一半.居住在斑块环境中的物种比连续生境中生存的物种可以更好地抵抗生境破坏带来的影响.

改进的求解独立成分分析参数的算法及应用

提出改进的求解独立成分分析参数的算法。该算法采用平均场近似原理,通过改变模型参数的限制条件,解决传统ICA算法中不能解决的问题。在图像特征的提取中,将模型中的混合矩阵和源信号均限制为非负,使提取的特征更为独立。利用语音信号、仿真图形及剑桥大学ORL人脸数据进行实验,从实验结果可以看出,改进的算法能有效地解决源信号数大于观测信号数的问题,同时该算法能分离出更独立的人脸五官特征,对ORL人脸识别结果分析表明,识别率从原来的87%左右提高到95%左右,也说明该算法比传统的算法更有利于进行图像特征提取及识别。

近似程度对强耦合磁极化子平均数特性的影响

本文应用幺正变换和线性组合算符法研究了极性晶体内强耦合磁极化子的平均数 与磁场Ｂ和温度Ｔ之间的依赖关系。讨论了在不同的近似计算程度情况下，磁极化子平均数与磁场和温度的特性。对ＲｂＣｌ晶体所作的数值计算结果表明：当计算的近似程度较低时，磁极化子的平均数随温度的升高而减小，但随磁场的加强而增大；当计算的近似程度较高时，磁极化子的平均数随温度的升高而增大，但随磁场的加强而减小。

基于平均场理论逼近的神经网络

本文试图从信息论观点导出平均场理论逼近的神经网络及其退火算法，证明ＡＭＦＴＡ（ＡｌｇｏｒｉｔｈｍｓｏｆＭｅａｎ－ｆｉｅｌｄｔｈｅｏｒｙａｐｐｒｏｘｉｍａｔｉｏｎ）和ＡＢＭ（ＡｌｇｏｒｉｔｈｍｏｆＢｏｌｔｚｍａｎｎｍａｃｈｉｎｅ）在一定条件下的等价性，既保留传统Ｂｏｌｔｚｍａｎｎ机算法的优点又提高了网络趋于稳态的收敛速度。

非线性复合介质电导的有效介质近似

在强外场作用下，复合介质的电输运性质服从非线性的本构关系．复合介质非线性电导率的计算相当复杂，在线性复合介质的理论框架内，已发展了多种有效介质近似方法．利用有效介质近似，可以导出计算有效偷运系数的简洁的解析公式．只要颗粒浓度在逾渗临界点以外以及颗粒和杂质的输运系数之比为有限的情况下，有效介质近似的计算都可以给出相当可靠的理论结果．因此，对于工程应用来说，有效介质近似是十分有用的工具．本文在非线性复合介质微扰展式解的基础上，发展了一种新的非线性有效介质近似理论文中导出的非线性有效电导率具有正确的低颗粒浓度极限．

驻波超导波态的数值研究

利用“超光”模型，描述了以能量密度为参量的超导波在驻波情况下的行为；对导出的积分方程进行了详尽的数值模拟，给出了“超光”出现的条件，并分析了基态能量密度ｕｇ和临界能量密度ｕｃ随光－声耦合强度λ的变化规律，从而为超导波的实验验证提供了数值依据．

磁场背景下有限温度NJL模型的手征性质

研究有限温度时均匀磁场背景下NJL模型的手征性质,计算不同磁场强度时有限温度和化学势下的手征凝聚和相图.利用玻色子化方法,得到具有辅助玻色子场的NJL模型拉格朗日密度,以此研究超出平均场近似的情形.通过使用最优化微扰论(OPT)方法,在微扰展开到一阶时,计入了部分高阶效应.计算结果表明,相变的性质与该模型在平均场近似下定性一致.相变线上存在两种不同类型的相变:在高温低化学势下是平滑的过渡,在低温高化学势下是一阶相变,相变存在临界终点(CEP).磁场增强会加剧手征对称性破缺,具有磁催化作用.随着磁场增强,CEP向相图的左上方移动,即对应的临界温度升高而临界化学势降低.

用均场逼近网络计算关联概率

数据关联问题是密集多回波环境下多目标跟踪中的一个关键问题。在固定温度参数T=1下,通过构造适当的能量函数,使Boltzmann机演化达平衡状态后,各神经元状态的平均值即为所要求的关联概率的近似值。在此基础上,提出了用均场逼近网络快速计算关联概率的新方法。仿真结果验证了本文方法的有效性。

不对称Hubbard模型与Mott金属-绝缘体相变

从标准Hubbard模型出发,对半充满Hubbard系统,采用Hubbard和Falicov Kimball近似处理,在讨论自旋为σ的电子运动时,忽略自旋为-σ的电子在格点间的跳跃,得到不对称哈密顿量,并运用平均场近似求得相应准粒子谱。在绝对零度和有限温度对结果作了分析,讨论了Mott金属-绝缘体相变的转变温度。