Effects of carrier density and interactions on pairing symmetry in a t_(2g) model

By utilizing the fluctuation exchange approximation method,we perform a study on the superconducting pairing symmetry in a t_(2g) three-orbital model on the square lattice.Although the tight-binding parameters of the model are based on Sr_(2)RuO_(4),we have systematically studied the evolution of superconducting pairing symmetry with the carrier density and interactions,making our findings relevant to a broader range of material systems.Under a moderate Hund’s coupling,we find that spin fluctuations dominate the superconducting pairing,leading to a prevalent spin-singlet pairing with a d_(x^(2)-y^(2))-wave symmetry for the carrier density within the range of n=1.5-4 per site.By reducing the Hund’s coupling,the charge fluctuations are enhanced and play a crucial role in determining the pairing symmetry,leading to a transition of the pairing symmetry from the spin-singlet d_(x^(2)-y^(2))-wave to the spin-triplet p-wave.Furthermore,we find that the superconducting pairings are orbital dependent.As the carrier density changes from n=4 to n=1.5,the active orbitals for superconducting pairing shift from the quasi-two-dimensional orbital dxy to the quasi-one-dimensional orbitals d_(xz) and d_(yz).

基于Thomas-Fermi-Kirzhnits模型的物态方程研究

本文针对丝阵Z箍缩等高能量密度物理实验的数值模拟研究,建立了一种适用温度、密度范围宽的三项式半经验物态方程.三项式半经验物态方程包括零温自由能项,电子热贡献项和离子热贡献项.零温自由能项采用多项式拟合的方法确定.多项式系数通过多项式计算的结果与高压缩比区域和压缩比为1时零温Thomas-Fermi-Kirzhnits模型计算的结果对应相等得到.离子对物态方程的热贡献采用一种准谐振模型,此谐振模型可以描述离子在固态相中的行为,并且在高温度、低密度区域趋近于理想气体物态方程.电子对物态方程的热贡献采用含温Thomas-Fermi-Kirzhnits模型计算.利用所建立的三项式半经验物态方程计算了铝的等温压缩曲线,并与实验数据做了对比.给出了很宽温度、密度范围内铝的压强,其数据与相应的SESAME数据库数据做了对比.

Thomas-Fermi模型含外电场作用的铝镁合金熵能的计算

本文基于Thomas-Fermi(TF)模型,提出外势场与原子内势场的作用,确定外势场对体系势场边界条件的影响,建立了外电场作用下的原子势场外边界条件。应用体积相加法,把单原子TF模型推广到化合物和固溶体。并以Al,Mg,Li等元素的单原子,Al-Mg固溶体,Mg5Al8化合物为例,计算和分析了电场作用对体系的熵能的影响。结果表明:熵能在整个电场区域内呈先减小后增大的变化趋势,并且边界势下和极板电压下的整体变化趋势一致,但零点处熵能的变化趋势不同。

Fermi Function and Its Applications

In this paper, we give a definition of the Fermi function, or the so-called Woods-Saxon potential, a well-known potential in nuclear physics;then, we give a few of its applications as examples. Some important integrals, which involve this function, are computed discussing the integrability and convergence of these integrals. Following, we derive formulae that encounter the above-mentioned function to get nuclear and generalized moments;the radial Fourier transformation is also exposed. Some related applications are then given that use such important integrals;in particular, we give the computation in conjunction with the problem of getting the optical-model potential for heavy-ion interactions at intermediate energies. Finally, we conclude with important remarks to do with the evolution of the subject.

Phase diagram of the Fermi-Hubbard model with spin-dependent external potentials: A DMRG study

We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin- dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde-Ferrell-Larkin-Ovchinnikov （FFLO） phase, a normal polarized phase, and a Bardeen- Cooper-Schrieffer （BCS） phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.

Two-vibron bound states in the β-Fermi-Pasta-Ulam model

This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.

Cosmic Bubbles

The present paper is inspired by the article “Ho’oleilana: An Individual Baryon Acoustic Oscillation?” published by R. B. Tully, C. Howlett, and D. Pomarède on Sep. 2023 [1]. They claim: Evidence is presented here for the discovery of a remarkably strong individual contribution to the baryon acoustic oscillation (BAO) signal at z = 0.068, an entity that is given the name Ho’oleilana. K. Dawson, co-spokesperson for Dark Energy Spectroscopic Instrument is more inclined to believe that this latest finding is something of a coincidence, a chance alignment that simply looks like a sphere with a radius around what you’d expect for a BAO [2]. In this paper, we provide a short summary of experimental observations of Boötes Void and Superclusters;discuss the main features of the developed Hypersphere World-Universe Model;introduce notions “Cosmic Voids” and “Cosmic Bubbles”;elaborate a mathematical framework for different types of Cosmic Bubbles (Hubble Spherical Bubble for the World, Disk Bubbles for Galaxies;Spherical Bubbles for Extrasolar Systems, Dark Matter (DM) Spherical Bubbles for Galaxies and Superclusters);make a conclusion that the Boötes is a DM Cosmic Bubble and suggest experiments, which confirm our conclusion.

Fermi-Pasta-Ulam模型中量子涨落对包络孤子的耗散效应

本文应用含时变分法原理研究一维Fermi-Pasta-Ulam模型,链中粒子的运动方程由含时变分法原理导出,在这个半量子研究中所考虑的量子效应是量子涨落。对于单个粒子,我们采用Jackiw-Kerman波函数。研究结论表明量子涨落能够发散、模糊化甚至破坏Fermi-Pasta-Ulam模型的非线性激发:包络孤子,量子涨落效应与有效普朗克常数有准指数关系。我们进一步发现与有效普朗克常数耦合,非谐耦合强度对量子耗散有联合效应,这种特有的联合效应可能是由Fermi-Pasta-Ulam模型独特的哈密顿量所导致。

利用Lanczos算法研究一维光晶格Fermi气体

研究了零温下一维光晶格Fermi气体随外加磁场和自旋轨道耦合(SOC)相互作用的变化特征。基于Fermi-Hubbard模型,采用Lanczos部分迭代法研究计算具有自旋轨道耦合(SOC)的一维费米链体系的基态波函数与基态能量,进一步得到超导配对序参量和磁化率的结果。计算结果表明,Lanczos迭代法在求解一维光晶格体系是收敛和有效的,外加磁场和SOC作用对BCS单重态的超导配对均具有抑制作用。另外在合适的磁场和SOC共同作用下存在Fulde-Ferrell-Larkin-Ovchinnikov(FFLO)相与BCS-FFLO混合相。通过与其他研究者的结果比较,体系特殊的相分布情况和非连续性相转变特征与较小的格点数可能相关。该结论对实验上探测BCS-FFLO混合相也具有指导意义。

Hypersphere World-Universe Model: Basic Ideas

Hypersphere World-Universe Model (WUM) envisions Matter carried from the Universe into the World from the fourth spatial dimension by Dark Matter Particles (DMPs). Luminous Matter is a byproduct of Dark Matter (DM) self-annihilation. WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) and Luminous Epoch (ever since for 13.77 billion years). Big Bang discussed in Standard Cosmology (SC) is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning DM Supercluster’s Cores and self-annihilation of DMPs. WUM solves a number of physical problems in SC and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Coronal Heating problem in solar physics—temperature of Sun’s corona exceeding that of photosphere by millions of degrees;Cores of Sun and Earth rotating faster than their surfaces;Diversity of Gravitationally-Rounded objects in Solar system and their Internal Heating. Model makes predictions pertaining to Rest Energies of DMPs, proposes New Type of their Interactions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.

Hypersphere World-Universe Model

Dirac’s themes were the unity and beauty of Nature. He identified three revolutions in modern physics: Relativity, Quantum Mechanics and Cosmology. In his opinion: “The new cosmology will probably turn out to be philosophically even more revolutionary than relativity or the quantum theory, perhaps looking forward to the current bonanza in cosmology, where precise observations on some of the most distant objects in the universe are shedding light on the nature of reality, on the nature of matter and on the most advanced quantum theories” [Farmelo, G. (2009) The Strangest Man. The Hidden Life of Paul Dirac, Mystic of the Atom. Basic Books, Britain, 661 p]. In 1937, Paul Dirac proposed the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”;and later added the notion of continuous creation of Matter in the World. The developed Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of matter creation. In this paper, we show that WUM is a natural continuation of Classical Physics and it can already serve as a basis for a New Cosmology proposed by Paul Dirac.

Hypersphere World-Universe Model: Evolution of the World

The main objective of this paper is to discuss the Evolution of a 3D Finite World (that is a Hypersphere of a 4D Nucleus of the World) from the Beginning up to the present Epoch in frames of World-Universe Model (WUM). WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) when only Dark Matter (DM) Macroobjects (MOs) existed, and Luminous Epoch (ever since for 13.77 billion years) when Luminous MOs emerged due to Rotational Fission of Overspinning DM Superclusters’ Cores and self-annihilation of Dark Matter Particles (DMPs). WUM envisions that DM is created by the Universe in the 4D Nucleus of the World. Dark Matter Particles (DMPs) carry new DM into the 3D Hypersphere World. Luminous Matter is a byproduct of DMPs self-annihilation. By analogy with 3D ball, which has two-dimensional sphere surface (that has surface energy), we can imagine that the 3D Hypersphere World has a “Surface Energy” of the 4D Nucleus. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Missing Baryon problem related to the fact that the observed amount of baryonic matter did not match theoretical predictions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements. In 2013, WUM predicted the values of the following Cosmological parameters: gravitational, concentration of intergalactic plasma, and the minimum energy of photons, which were experimentally confirmed in 2015-2018. “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (Nobel Prize in Physics 2020) made by Prof. R. Genzel and A. Ghez is a confirmation of one of the most important predictions of WUM in 2013: “Macroobjects of the World have cores made up of the discussed DM particles. Other particles, including DM and baryonic matter, form shells surrounding the cores”.

Dynamical Modeling of the Nuclear Fission Process at Low Excitation Energies

Two recipes for modeling the dynamics of the nuclear fission process are known in literature. The underlying equations contain the driving, dissipative, and random forces. The two recipes are mostly different in the prescriptions for the driving force. In this work we carefully compare these driving forces and the resulting fission rates. It turns out that the rates may be very close or strongly different depending on the value the shell correction to the nuclear deformation energy. We give arguments in favor of one of the recipes.

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region.The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.

Ferromagnetic transition of a spin-orbit coupled dipolar Fermi gas at finite temperature

We study the ferromagnetic transition of a two-component homogeneous dipolar Fermi gas with 1D spin-orbit coupling(SOC) at finite temperature.The ferromagnetic transition temperature is obtained as functions of dipolar constantλd,spin-orbit coupling constant λSOC and contact interaction constant λS.It increases monotonically with these three parameters.In the ferromagnetic phase,the Fermi surfaces of different components can be deformed differently.The phase diagrams at finite temperature are obtained.

About One Discrete Mathematical Model of Perfect Fluid

In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic model of an ideal fluid. The results of computational experiment to simulate various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation of particles in a region, various kinds of eddy streams, with the quite unexpected statistical properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found. We build and study the flow in which the velocity of the particles is calibrated. It was possible using the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce any prescribed image by manipulating the parameters of the interaction. Calculations of the flows were performed with using MATLAB software package according to the algorithms presented in this article.

学生解决费米问题和数学建模问题的认知差异研究

研究学生解决费米问题和数学建模问题过程中的认知差异及原因,是探讨将费米问题引入数学建模教学可行性的基础.解决费米问题与数学建模问题,学生都需要基于现实情境假设并构建模型,但是由于问题结构不同,学生在解决两类问题时存在一些认知差异:在知觉启动环节,学生能迅速整体感知数学建模问题,但难以立即提取费米问题的相关信息;在现实问题表征环节,学生更容易错误理解费米问题的信息.如果知识图式不够丰富,学生表征数学建模问题时就可能会遇到困难,但能顺利表征费米问题.受“基于问题结构”的思维定势影响,学生会倾向于过度简化假设费米问题,而对数学建模问题的假设相对较合理.

Investigation of quark distributions in a family of pentaquarks using the Thomas-Fermi quark model

Using the Thomas-Fermi quark model,a collective,spherically symmetric density of states is created to represent a gas of interacting fermions with various degeneracies at zero temperature.Over a family of pentaquarks,uudcc,color interaction probabilities were obtained after averaging over all the possible configurations.Three different functions are developed for light,charm,and anti-charm quarks and are assumed to be linearly related by some proportionality constants.Interesting patterns of quark distributions are observed while analyzing the quark function consistency conditions for such constants.

Al-Li-Mg合金电场下自由能的TF方程计算

基于Thomas-Fermi(TF)模型,确定电场作用下的内势场边界条件,建立了电场作用下单原子、化合物,固溶体、实际工业合金的自由能计算方法,系统地定量计算研究了电场作用下自由能的变化趋势。结果表明:单原子自由能变化趋势在电场作用下是关于非零电场对称的,并且不同元素的自由能对电场的敏感性不同,Al,Mg,Li3元素在正电场一侧的敏感性依次为Al,Li,Mg;在负电场一侧的敏感性依次为Al,Mg,Li。电场作用下Al3Li化合物和固溶体Al-2.14%Li(原子分数,下同)的自由能在460K和800K表现出不同电场对称性和电场敏感性。在两种温度下,Al-2.14%Li固溶体自由能的电场敏感性要高于化合物Al3Li。而且在800K高电场下固溶体Al-2.14%Li的自由能明显高于化合物Al3Li的自由能,在460K相同的电场下,化合物的自由能低于固溶体的自由能。1420合金自由能的变化趋势是关于零电场对称的,时效电场下1420合金的拉伸性能也是关于零电场对称的。

脉冲放电等离子体电子激发温度发射光谱诊断

利用微量Ar的发射光谱,对标准大气压N2脉冲流光放电等离子体特性进行了实验研究.在对所得Ar原子荧光谱线归属的基础上,分别采用谱线相对荧光强度比值法,玻尔兹曼曲线斜率法和费米-狄拉克布居分布模型法3种计算方法,对标准大气压N2脉冲流光放电等离子体电子激发温度进行分析比较.结果表明:采用玻尔兹曼曲线斜率法和费米-狄拉克布居分布模型法计算得到的电子激发温度非常接近,分别为(7 474±500)K和(7 480±500)K,说明本研究所涉及的脉冲流光放电等离子体至少接近局部热平衡.