Numerical Simulation Solution of the BCS Pairing Problem

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2^N-dimensional matrix is reduced to the polynomial problem of N-dimensional matrix. It is essential to validate this method on a real quantum computer and is helpful to understanding the many-body quantum theory.     

Gauge technique and BCS theory of superconductivity

Summary The gauge technique in unbroken (exact) relativistic quantum electrodynamics is applied to the nonrelativistic BCS theory exhibiting spontaneously brokenU(1) gauge invariance. In addition to the BCS-type solution, we find an interestingnew solution forweak coupling exhibiting ahigh T _c. The authors of this paper have agreed to not receive the proofs for correction.     

超导BCS理论的建立

介绍了巴丁、库珀和施里弗的生平,回顾了BCS理论的建立过程,综述了BCS理论建立的影响和意义,以及由此带给人们的有益启示.     

Pairing mechanisms and anisotropic superconductivity in layered crystals

A brief outline of the generalized BCS pairing theory is presented. The pairing of carriers can be due to the exchange of lattice-phonons or due to the exchange of electronic charge-density and spin-density excitations. It is argued that anisotropic physical properties in the normal as well as superconducting states in the new high-T_c materials are crucual in the development of any realistic theoretical approach, and in comparison of experimental results with correct BCS predictions involving superconductivity in layered crystals. The possibility of the break-down of the mean-field approximation is also discussed. As of now, the generalized BCS pairing approach is the only realistic microscopic theory available which may be applied to high-T_c superconductors.     

热动力学问题的数值计算

 对含热传导的流体动力学方程组，用有限元方法进行数值求解。采用傅里叶热传导计算热流、用热流连续条件计算单元间接触面的温度、用三角形传热法计算体单元表面的热流，考虑各向同性弹塑性流体材料模型、三项式物态方程和导热系数与状态的相关性，给出了傅里叶热传导、接触传热、热应力应变效应、以及混合物冲击压缩特性等算例。对混合物冲击温度的数值模拟表明，小颗粒混合物在冲击压缩过程中，颗粒间的温度有差别、稍有波动，并随时间趋向于一致，以至热平衡。     

Specific heat of a BCS superconductor

By expressing the free energy as an appropriate temperature integration over the square of the BCS energy gap function and by substituting simple but accurate analytic expressions for the latter, corresponding expressions are obtained for the specific heat in the superconducting state. In the upper portion of the temperature range, the ratio of the specific heats in the superconducting and normal states is 2.43 (1 + 0.936 in t), to better than one per cent accuracy, where t is the reduced temperature. Thus, the semilog plot of temperature versus the ratio of specific heat to temperature is a straight line over a large portion of one decade of specific heat. Corresponding expressions of similar simplicity and accuracy are obtained for the middle and low temperature ranges.     

用BCS理论计算稀土核转动惯量的奇偶差

用BCS理论计算了稀土区偶偶核和奇A核的转动惯量.计算结果表明,尽管转动惯量的计算值系统地小于实验值,但实验上观测到的转动惯量奇偶差的大幅度变化能够用BCS理论定性地描述. 这个结论与人们普遍认为的BCS理论给出的奇A核转动惯量应比相邻的偶偶核基态转动惯量大15%的看法相悖,但却证实了20多年以前Gregory和Volkov等人得出的结论,有助于人们在BCS平均场理论框架下理解正常形变核中出现全同带的现象.     

The large-deviation principle and the BCS model

The BCS model is investigated by the functional integrals method and Euclidean quantum field theory technique. It permits us to apply some version of the Large Deviation Principle and get the exact solution which was obtained earlier by the approximation Hamiltonian method.     

A study of particle number fluctuation under BCS theory

Particle number fluctuations in BCS theory are studied with the relativistic mean-field theory and the shell effects of particle number fluctuations are first discovered. By analyzing the relative errors of the particle number fluctuations, we find that the particle number fluctuations are relevant with the odd-even character. We later apply this method to the examination of the new shell structure, showing that N = 184 for the neutron is indeed a new closed shell.     

Quantum entanglement and pairing correlation in the reduced BCS pairing model

Using the particle-hole version of the density-matrix renormalization-group technique, the pairing correlation and the quantum entanglement of the reduced BCS pairing model are investigated. Both of them behave smoothly from the weak to the strong coupling regimes. A convergence radius (∼1/ln Ω) of condensation energy is detected by the first order derivative of the block-block entanglement. Furthermore, the block-block entanglement in the strong coupling regime shows distinct size dependence, and a logarithmic volume law is suggested numerically.     

The ground state and the thermodynamics of an extended BCS model of superconductivity

The thermodynamics of an extended BCS model of superconductivity is investigated. A physical system is described by a Hamiltonian containing the BCS interaction and an attractive four-fermion interaction. The four-fermion potential is caused by attractions between Cooper pairs mediated by the phonon field. The weakness of this potential allows the use of perturbation theory. The perturbation expansion was restricted to the first order because in the ground state the second order terms are not larger than 0.5 percent of first order correction for parameters used for calculations. The BCS Hamiltonian is an unperturbed one. The ground state and the thermal properties are examined. As a result the jump in the specific heat is higher than that in the BCS case. Moreover, the squared critical field is larger than the corresponding one in the BCS theory. Additionally, we show connections with the Bogolyubov's mean field approach used earlier in order to investigate general physical consequences of the model.     

Dynamics and effective actions of BCS superconductors

We derive the effective dynamical theory for BCS superconductors, based on the effective action formalism. Both the metallic regime and the superconducting regime are studied in the clean and dirty limit. The full electrodynamics of the problem is formulated in a manifestly gauge-invariant and transparent way. Furthermore, we consider the effect of particle-hole asymmetry in the band structure, and discuss its consequences for vortex dynamics and the topological term in the effective action. The effective action is the starting point for treating (quantum-) dynamical problems involving BCS superconductors. Received 23 November 1998     

Nucleon aPF2 Superfluid Pairing Gap in Asymmetry Nuclear Matter

The 3 P F2 superfluidity of neutron and proton is investigated in isospin-asymmetric nuclear matter within the Brueckner-Hartree-Fock approach and the BCS theory by adopting the Argonne V14 and the Argonne V18 nucleonnucleon interactions. We find that pairing gaps in the 3PF2 channel predicted by adopting the AV14 interaction are much larger than those by the AV18 interaction. As the isospin-asymmetry increases, the neutron 3 pF2 superfluidity is found to increase rapidly, whereas the proton one turns out to decrease and may even vanish at high enough asymmetries. As a consequence, the neutron 3pF2 superfluidity is much stronger than the proton one at high asymmetries and it predominates over the proton one in dense neutron-rich matter.     

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length and a large critical temperature, , appropriate for some high- materials. The BCS gap, , and specific heat as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below in p and d waves. Received: 18 July 1997 / Revised: 8 September 1997 / Accepted: 29 September 1997     

Numerical Solution of the Four-Anyon Problem

By making use of the Talmi-Moshinsky transformation bracket, -the Schrödinger equation for four anyons in configuration space has been solved variationally to obtain the eigenenergies and eigenfunctions. The low-lying states have been presented as functions of the statistical parameter. We illustrated how the bosonic states evolve continuously into the fermionic states.     

对关联对核基态和集体激发态性质的影响

基于相对论平均场和BCS理论,研究了共振连续对奇特核对关联性质的影响. 利用S矩阵方法，通过设定合理的散射态边界条件来得到单粒子共振态的能量和宽度. 通过引入连续态能级密度的方法来处理共振态宽度对核对关联的贡献. 计算结果显示合理地处理共振态对对关联性质的贡献在研究滴线附近核性质时很重要. 它可以影响中子的对隙、费米能级、对关联能以及总结合能. 其次,基于RMF+BCS基态,采用线性响应理论给出了描述开壳核集体激发态性质的准粒子相对论无规位相近似理论. 并且将该方法应用于开壳核120Sn的各种同位旋标量集体激发态性质的研究中. 研究表明：对关联对核的集体激发性质的影响主要表现在低能集体激发态上,考虑对关联后的相对论无规位相近似理论能够很好地再现低能集体激发的实验结果.     

Liquid Model of Phase Transition from Quark-Gluon Phase to Hadron Phase on Analogy of BCS Theory

A phenomenological model of the transition from quark-gluon phase to hadron phase is presented on the analogy of BCS theory. The massive current-quarks constitute the quark Cooper-pair, i.e., the hadron at T_c = 150~200 MeV, The order parameter of qq-pair takes a value in the range from 0.4 to 0.2 GeV. An experimental verification method of the present model in the heavy-ion collision is proposed.     

Specific heat jump in BCS superconductors

An exact analytical expression for the specific heat jump at the critical temperature T_c has been obtained directly from the BCS gap equation for any shape of the energy dependent electronic density of states (DOS). We consider a model which takes into consideration electron-electron repulsion, formulated in the Hubbard model along with the electron-electron attraction due to electron-phonon interaction in the BCS formalism. We have analyzed this expression for constant as well as for the Lorentzian forms of DOS. It is shown that the constant DOS in the simple BCS theory cannot explain the large values of , found in some superconductors. The specific heat versus temperature curve has been found to have a peak, similar to that of Eliashberg theory of superconductivity. The influence of repulsive interaction is very small and occurs mainly at higher temperatures. Received: 26 January 1998     

Dynamics of the open BCS model

The dynamics of the strong coupling BCS model, considered as an open system interacting with a thermal bath, is solved rigorously and explicitly in the weak coupling limit and in the infinite-volume limit. The BCS system goes from the normal phase to the ordered phase by bifurcation. Fluctuations around trajectories of intensive observables are Gaussian and Markovian. Thermodynamic phases are global attractors in the physical domain. Structural stability is discussed. The model provides an example of a nonequilibrium statistical mechanical system with phase transition whose irreversible macroscopic dynamics can be calculated exactly from the underlying Hamiltonian quantum mechanics.     

Dimensionality and Finite Number Effect on BCS Transition of Atomic Fermi Gas

The effect of finite number and dimensionality has been discussed in this paper. The finite number effect has a negative correction to final temperature for 2D or 3D atomic Fermi gases. The changing of final temperature obtained by scanning from BEC region to BCS region are 10% or so with N≤10³ and can be negligible when N>10³. However, in 1D atomic Fermi gas, the effect gives a positive correction which greatly changes the final temperature in Fermi gas. This behavior is completely opposed to the 2D and 3D cases and a proper explanation is still to be found. Dimensionality also has a positive correction, in which the more tightly trapping, the higher final temperature one gets with the same particle number. A discussion is also presented.