Surface induced mixed state of a superconducting film

Presented in this paper is a theoretical analysis of a planar surface induced mixed state for a superconducting film in parallel applied field. An analytical solution of the internal magnetic field is obtained based on Saint-James and de Gennes' order parameter in a film. An expression of Gibbs free energy per unit volume without restriction of a geometry is derived from non-linear Ginzburg-Landau (GL) equation in terms of a renormalized GL parameter and a modified geometric factor. Based on the Gibbs free energy, a phase diagram of distinguishing a first and second order phase transition for a type I superconducting film is calculated. The numerical results for exact solutions of spatial variation of order parameter, current density and internal magnetic field in the film geometry in parallel applied field case are presented. Near the upper critical field, the first entry of an applied field in the film exhibits a laminar structure.     

The functional renormalization group and O(4) scaling

The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry-breaking external field. We perform a set of approximations to formulate and solve the FRG flow equation in the presence of fermionic degrees of freedom and test their influence on the O(4) critical properties expected in the quark-meson model. Within this scheme, the critical scaling behavior of the order parameter, its transverse and longitudinal susceptibilities as well as the correlation lengths near the chiral phase transition are computed for vanishing baryon density. We focus on the scaling properties of these observables at non-vanishing external field when approaching the critical point from the symmetric as well as from the broken phase. We confront our numerical results with the Widom–Griffiths form of the magnetic equation of state, obtained by a systematic ε expansion of the scaling function.     

Equations of state along the road to Arrott's last plot

A modification of the Weiss theory of ferromagnetism is used to create an approximate equation of state that relates the magnetization, field and temperature. The high-temperature susceptibility, the critical region and the temperature dependence of the spontaneous magnetization to low temperature are found by making an approximation for the inverse Brillouin function and then adding critical exponents in the proper places. The coefficient of the Weiss effective field is treated as dependent on the magnetization, introducing an additional parameter. This equation of state is applied to results from studies of iron whiskers.     

Evaluation of critical current based on a new transition concept

The critical current of high-temperature superconductor (HTS) tapes depends on temperature, magnetic field, and flux angle against the tape. Analyzing the performance of an HTS coil relies on the critical current equation, which has these dependencies. To date, the critical current equation has been obtained by fitting the measured data. However, this fitting method requires the time-consuming and laborious work of measuring the tapes. In this study, based on a new transition concept in applying a magnetic field, we show how to obtain the critical current equation, while keeping the temperature constant. From the wave function of the Cooper pair which distributes along a magnetic flux quantum, a wave function at the transition state is obtained; this yields the wave functions with perpendicular and parallel magnetic components against the tape. Combining these wave functions yields the conclusive critical current density equation. To confirm the accuracy of this equation, used Bi-2223/Ag tapes, it was compared with the measured critical current under various magnetic fields and flux angles; it was found that they agree well. The parameters of this equation can be obtained by measuring the perpendicular/parallel critical magnetic field component. This equation does not require fitting the measured data, therefore, it can be employed with any Bi-2223/Ag tape.     

Field-theoretic approach to critical dynamics far from equilibrium

The field-theoretic approach to critical phenomena is extended to deal with critical dynamics far from equilibrium. In particular, the macroscopic evolution equation for the average order parameter is derived in a manner parallel to the derivation of the equation of state. The method is illustrated by deriving the scaled macroscopic equation of motion for the timedependent Ginzburg-Landau model near the critical point for dimensionality near four.     

渗透胁迫下萌发小麦种子超弱光子辐射的变化及意义

为了将生物超弱光子技术应用于萌发过程中小麦种子的抗旱性评价,采用聚乙二醇处理萌发的小麦种子,跟踪测量了正常和渗透胁迫下小麦种子萌发过程中的超弱光子辐射,得到了小麦种子萌发过程中超弱光子辐射的自发发光和延迟发光信号.通过建立延迟发光动力学方程和数学拟合获得了种子萌发过程中延迟发光初始光强I（0）、衰减参量β、相干时间τ和延迟发光积分强度I(T),根据延迟发光积分强度和自发发光的生物学意义构建了用于描述细胞状态及其有序性的状态参量和序参量.实验结果发现:小麦种子萌发过程中,自发发光和延迟发光积分强度呈现阶跃式增长,细胞系统的状态参量和序参量也呈现阶跃式的增长,渗透胁迫抑制了这种增长,提示基于光子辐射的细胞系统的状态参量和序参量有可能作为种子抗旱性评价的物理指标.     

Role of charge fluctuation in Q1D organic superconductor (TMTSF)2ClO4

We have theoretically investigated the spin and charge fluctuations in the quasi-one dimensional organic superconductor (TMTSF)₂ClO₄. Using the extended multi-site Hubbard model, which contains four sites in a unit cell and the transfer energies obtained by the extended Hückel method, we calculate the linearized gap equation with the random phase approximation, to find novel order parameters of superconductivity due to several kinds of charge fluctuations induced by the anisotropic intersite repulsive interactions. For the singlet state, the order parameter with line nodes appears in the case of the strong charge fluctuation, while the order parameter with anisotropic gap suggested by Shimahara is reproduced in the spin fluctuation. The triplet state is also obtained for the wide parameter range of repulsive interactions due to a cooperation between charge and spin fluctuations.     

Order parameter of layered superconducting structures

It is suggested that the order parameter and the critical temperature in an S-N structure be described on the basis of the microscopic Ψ theory, modeling the metal in the normal state by the Ginzburg-Landau equation with a negative coefficient a. It is shown that at a contact between layers the order parameter in the layer whose temperature is below the critical temperature induces an order parameter in the other layer whose temperature is higher than the critical temperature.     

Spectral density method for an anisotropic linear chain

The spectral density method is used to study the thermodynamic properties of an anisotropic antiferromagnetic Heisenberg linear chain in an external magnetic field. Insecond order approximation without the decoupling procedure for the two particle correlation function, we are able to obtain many results in terms of both the temperature and the magnetic field for different values of the anisotropy parameter. The ground state of the model is investigated and the singular behaviour of some thermodynamic quantities near the critical field is determined. In particular, explicit analytical solutions are given for small anisotropy parameters. Our results are compared with the ones obtained by means of other methods and some exact results are reproduced.     

Molecular properties and potential energy function model of BH under external electric field

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.     

Fulde-Ferrell-Larkin-Ovchinnikov state in layered superconductors

The phase diagram of a layered superconductor in a large parallel magnetic field is calculated. This includes a calculation of the lower critical field beyond which the superconductor is in the FFLO-state and possesses a spatially modulated order parameter and spin polarization. The order parameter, spin polarization, free-energy density, and phase boundaries of this unconventional superconducting phase are evaluated numerically in the complete B–T plane. The analysis suggests that the transition at the lower critical field is of second order, and not of first order, as previously assumed. The order parameter of the FFLO-state merges continuously into the uniform superconducting state.     

The ratio of normal state to superconducting state of spin lattice relaxation rate of unconventional superconductors

In this research, we derive a simple expression for the ratio of normal state superconducting state of spin lattice relaxation rate of unconventional superconductors from the BCS weak-coupling equation. The unconventional superconductors we consider have three types of order parameters as d-wave, ³He A-phase and p-wave three-dimensional order parameter that had been done before by Parker and Haas [D. Parker, S. Haas, Physical Review B 75 (2007) 052501]. After using some numerical approximations and some boundary conditions, we can find the ratio of normal state to superconducting state of spin lattice relaxation rate in power series of temperature dependent order parameters and temperature. Our numerical calculations show the coherence peak below critical temperature clearly that are consistent with Parker and Haas [D. Parker, S. Haas, Physical Review B 75 (2007) 052501]. These results do not agree with the believed that the coherence peak is the only property of s-wave superconductor. However from our calculation, we can conclude that the unconventional superconductors can show the coherence peaks.     

Phase transitions induced by microscopic disorder: A study based on the order parameter expansion

Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two which describe the fluctuations around this mean value. The method is based on a systematic perturbation expansion and can be applied around the vicinity of the homogeneous state. With this tool we analyze phase transitions induced by microscopic disorder in three prototypical models of phase transitions which have been studied previously in the presence of thermal noise. We study how macroscopic order is induced or destroyed by time-independent local disorder and analyze the limits of the approximation by comparing the results with the numerical solutions of the self-consistency equation which arises from the property of self-averaging. Finally, we carry on a finite-size analysis of the numerical results and calculate the corresponding critical exponents.     

A JUSTIFICATION FOR THE SCALING OF THE THOM-SYSTEM

In the present paper we discuss the critical behavior of Thornsystem using Catastrophe Theory. The universal critical asymptotic form of the family of free energy functions for Thomsystem with one order parameter and two field parameters is obtained. The expressions of critical exponents, the scaling laws, and the scaling hypotheses are all derived from this universal asymptotic form.     

Phase transition and critical properties of spin-orbital interacting systems

Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin-orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin-orbital order-disorder transition is far from the second-order, rather, it is more close to the first-order. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.     

CO2气、液、固三相饱和态下pVT的计算

本文基于分子聚集理论和硬球引力场模型应用分子热力学方法导出CS-vdW状态方程,应用上述方程计算了CO2气-液和气-固平衡相的饱和态下pVT性质.取得了很满意的结果.本方法的优点是使用简便,可供工程计算使用.     

Thom系统标度性的证明

本文应用突变论(catastrophe theory)证得了Thom系统自由能函数族的普适的临界渐近形式,并从它推导了临界指数公式,标度律和标度假设。 关键词：     

On a leveraging effect of weak azimuthal inhomogeneities explaining the nonuniqueness of critical Maier-Saupe order parameters

The Maier--Saupe theory of liquid crystals predicts a unique critical order parameter for the transition point of isotropic--nematic phase transitions. Experimental studies have shown that critical order parameters are shifted away from that unique value. We show that micro-defects and weak azimuthal inhomogeneities can result due to a leveraging effect in the experimentally observed macro-shifts of the critical order parameter. We demonstrate the leveraging effect by computing the corresponding micro-shifts of the order parameter in the isotropic phase with the help of an effective order parameter. Our approach accounts for critical order parameters observed in experimental studies which is explicitly demonstrated for methyl-deuterated para-azoxyanisole (PAA-d₆), 4-n-pentyl-4′-cyanobiphenyl (5CB), N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Finally, in line with the effective order parameter approach and the dynamical mean field approaches by Hess, Doi, and Edwards, predictions are derived that provide novel testbeds for experimental studies.     

含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度

利用张量网络表示的无限矩阵乘积态算法研究了含有Dzyaloshinskii-Moriya (DM)相互作用的键交替海森伯模型的量子相变和临界标度行为.基于矩阵乘积态的基态波函数计算了系统的量子纠缠熵及非局域拓扑序.数据表明,随着键交替强度变化,系统从拓扑有序的Haldane相转变为局域有序的二聚化相.同时DM相互作用抑制了系统的二聚化,并最终打破系统的完全二聚化.另外,通过对相变点附近二聚化序的一阶导数和长程弦序的数值拟合,分别得到了此模型相变的特征临界指数a和b的值.结果表明,随着DM相互作用强度的增强, a逐渐减小,同时b逐渐增大. DM相互作用强度影响着此模型的临界行为.针对此模型的临界性质的研究,揭示了量子自旋相互作用的彼此竞争机制,对今后研究含有DM相互作用的自旋多体系统中拓扑量子相变临界行为提供一定的借鉴与参考.