Further Establishment of the Field Perturbation Theory of the Pseudogaps in HTSC

Here I establish the field perturbation theory of pseudogaps in HTSC. The proposed ground state suggests an internal particle-hole field, which is normal to nesting surfaces, and having twice the Fermi wave number. It is proved that the system violates momentum conservation by the wave vector of this internal field. This violation applies to the quasi-particle propagators, as well as to the interactions. Interaction vertices via the Pauli matrix-τ₁ are established. This, in turn, establishes the validity of the pseudogap Hartree self-energy.     

The Pseudogaps of HTSC

The problem of the pseudogaps in oxide HTSC is analyzed by means of the off-diagonal propagators, in analogy with the method of Nambu in superconductivity. We conjecture that the small pseudogap is obtained as the Fock diagram and the large pseudogap as the total off-diagonal self-energy (which is the sum of the Hartree diagram and the Fock diagram). We obtain real gap for undoped materials, and pseudogaps (with states in the gap) for doped and conducting materials. We find that disorder is essential for the results of the doped materials.     

The Pseudogaps of HTSC

The problem of the pseudogaps in oxide HTSC is analyzed by means of the off-diagonal propagators, in analogy with the method of Nambu in superconductivity. We conjecture that the small pseudogap is obtained as the Fock diagram and the large pseudogap as the total off-diagonal self-energy (which is the sum of the Hartree diagram and the Fock diagram). We obtain real gap for undoped materials, and pseudogaps (with states in the gap) for doped and conducting materials. We find that disorder is essential for the results of the doped materials.     

The Field Perturbation Theory of the Double Correlated Phase in HTSC

The double-correlated phase in HTSC, and its treatment by field perturbation theory, is being established. In particular, we define the ground state, the quasiparticle excitations, and construct an appropriate field. We also derive the unperturbed Hamiltonian, and the propagators for the unperturbed state. Then, we discuss the perturbation Hamiltonian, and show that the Hartree Diagram is significant for both the pseudogap and the superconductive order parameters, and suggest that it yields the major contribution to these parameters.     

Complementary Analysis of the Field Perturbation Theory of Superconductivity

We reexamine the Nambu–Gorkov perturbation theory of superconductivity. We suggest that any field perturbation theory of superconductivity should be based on the Bogoliubov–Valatin (BV) quasi-particles. We show that two such different fields (and two additional analogous fields) may be constructed on the basis of this suggestion. The Nambu field is only one of them. For the field that is different than Nambu’s, the coherence field, the interaction is given by means of two interaction vertices that are based on the Pauli matrices τ₁ and τ₃. Consequently, the Hartree integral for the off-diagonal pairing self-energy may be finite, and in some cases large. We interpret the results in terms of conventional superconductivity and also discuss briefly the possible implications to HTSC.     

Diffusion of the superconducting transition in HTSC

In the present study it is shown that the transition to the superconducting state can be described within the framework of the phenomenological theory of diffused phase transitions, due to the structural material heterogeneity. The paraconductivity due to the appearance of fluctuating Cooper pairs at temperatures above T_c, demonstrates 2D–3D crossover, which also occurs in a certain temperature range, located above the superconducting transition interval.     

The Origin of the Pseudogap in Underdoped HTSC

Here, the origin of the pseudogap in HTSC is attributed to the modulated antiferromagnetic (AFM) phase, whose preliminary version has been sketched recently by the present author (in J. Super. Nov. Mag. 22:517, 2009). Starting from the t-J Hamiltonian, I show that the formal failure of the perturbation theory leads to a transformation to the pseudogap phase. This phase is characterized by the aggregation of the holes into rows and columns, which in turn results in two internal fields. The first is the modulated AFM field, whose main evidence comes from Neutron scattering experiments. The second internal field is made up by the checkerboard charge density waves that have been observed by scanning tunneling measurements. The present paper deals mainly with the internal field of the first type, and discusses the second type only tentatively. Formalism is derived that yields the ground state, the internal field, the Hamiltonian, and the propagators of the condensed phase. Our results resolve the presumably inherent self-contradictory concept of pseudogap. It is shown that the excitation energy spectrum is gapless despite the order parameter that is inherent to the condensed system. In addition, it is shown qualitatively that our model predicts “Fermi surface” that is in agreement with the experiment.     

Spectral Properties of the Bose-Hubbard Model Within the Cluster Perturbation Theory in X-Operators Representation

We study the two-dimensional ultracold Bose gas in optical lattice. We use cluster perturbation theory based on Hubbard X-operators to calculate the spectral function and phase diagram of Bose-Hubbard model which is minimal model to describe behavior of ultracold gases in optical lattices. We have analyzed spectral properties of spinless bosons in a square lattice taking into account the short-range correlation.     

Analysis of the high-temperature behavior of paraconductivity in HTSC

The Aslamazov-Larkin term of fluctuation conductivity in two-dimensional superconductors is extended to arbitrary temperatures for intermediate scattering times by including the dynamic and short wave-length contributions side by side with the non-local effects. Numerical results for a few different values of are presented.     

Thermodynamic Properties of Sutherland Fluids from an Analytical Perturbation Theory

Analytical expressions are obtained for the thermodynamic properties of fluids with potentials consisting of a spherical hard core plus an attractive tail of the form 1/r (Sutherland fluids). To this end, use is made of the Barker–Henderson perturbation theory together with an analytical expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid. This expression was derived previously on the basis of the analytical solution of the Percus–Yevick integral equation theory. The results are compared with available simulation data for a wide range of densities, temperatures, and values of the potential parameter . The overall agreement is good, and the accuracy is similar to that obtained using more accurate solutions for the radial distribution function of the hard-sphere fluid leading to nonanalytical expressions for the thermodynamic properties of the fluid considered.     

基于微扰理论的静电电子透镜的缺陷电场计算

研究了用于计算电子光学系统的缺陷电场和容差的微扰理论。基于微抗原理，推导了计算静电电子透镜由于电极偏心、倾斜和加工不圆造成的电场变化及其旁轴多极场展开函数的九点有限差分公式，编制了计算软件。建立了两个电场解析模型，通过该模型的解析解与数值计算结果的对比，证实了算法及软件的正确性，并据此讨论了微扰理论用于容差计算的适用范围。计算了几个静电电子透镜的例子，给出了不同电极缺陷的电位分布和微扰多极场分布。     

重庆市GPS基线场的建立

近年来,GPS以其显著特点,在我国成功地应用于大地测量,工程测量,航空摄影测量等多种学科。为保证GPS的定位监测精度,需要建立测量型和导航型全球定位系统GPS接收机等测绘仪器校准用大地基线场。     

基于奇异摄动理论的电驱动机器人神经网络控制

在驱动回路电容较小的情况下,对电驱动刚性机器人操作手的轨迹跟踪问题,提出了一种基于奇异摄动理论的神经网络控制设计方法。稳定性分析表明系统跟踪误差最终一致有界,数值实验验证了所提的算法的可行性和有效性。     

The Inward Dispersion of the Neutron Scattering Experiments in HTSC Cuprates

The theory of the high-temperature superconducting cuprates, which is based on the condensation of holes into strings in checkerboard geometry, was successful to explain the elastically scattered neutrons by spin waves. Here, it is extended to analyze the inward dispersion curve of its inelastic counterpart, up to the resonance energy (E _res). This extension is done by applying the perturbation theory of the linear response to the condensed strings. The approximated susceptibility is derived by means of the ring diagram. The dispersion relation is obtained from the dispersion of the poles of the susceptibility integral. It is found that the particle-anti-particle pair that yields the susceptibility is the time reversal pair where the particle momentum is k in phase A and the anti-particle momentum is ?k in phase B. The dispersion is found to be in agreement with experiment, subject to some suggested corrections. The weak intensity by the resonance energy, as well as the dispersion, is speculated to be modified due to interference with spin waves that are caused by direct spin flip, as in the undoped mother materials.     

Flux-Line Entanglement as the Mechanism of FLL-Melting Transition in Anisotropic HTSC

The mechanism of the flux-line-lattice (FLL) melting in anisotropic high-T _c superconductors in B is clarified by Monte Carlo simulations of the 3D frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature T _m , while no sharp change can be found in the number and size distribution of vortex loops around T _m . Therefore, the origin of this melting transition is the entanglement of flux lines. Scaling behaviors of the melting temperature T _m are consistent with this one-dimensional character of the entanglement mechanism of the FLL melting. That is, T _m does not depend on the system size in the ab plane, while it is scaled by the system size along the c axis, L _c , as T _m(L _c ) – T _m() L _c ^-d , d = 1.     

The mechanism of hole carrier relaxation in HTSC

The nature of hole carriers in high-T_c superconductors (HTSC) and mechanism of their relaxation are considered on the base of the HTSC electronic spectrum model suggested before. The model proposes that the distinctive feature of HTSC electronic spectrum is the pair level placed at the top of valence band. It is shown that this feature may account for the peculiarities of transport and optical properties observed in experiment.     

Analytic Equation of State for Lennard-Jones Fluids Based on the Ross Variational Perturbation Theory

By using a previously developed analytic expression for the radial distribution function of hard spheres, a simple analytic equation of state (EOS) for fluids with a continuous Lennard-Jones potential is established based on Ross's variational perturbation theory. The main thermodynamic quantities have been analytically derived, the resulting expressions are surprisingly simple, the variational procedure is greatly simplified, and the calculations are absolutely convergent. The numerical results are compared with the Monte-Carlo data and the original Ross variational theory. It is shown that the precision of the analytic EOS is as good as the original non-analytic one, and their applicable range is believed identical. A comparison with the recently proposed mean-sphere-approximation theory shows that the analytic equation of state developed here has wider applicability and precision.     

NMR Study on the Electronic Structure of the Vortex State in HTSC

By using spatially-resolved NMR method, we observed nuclear spin-lattice relaxation rate (1/T ₁) of the vortex state to probe antiferromagnetic correlations at the vortex core. We found that the temperature dependence of 1/T ₁ shows a peak, which results from a local antiferromagnetic ordering of Cu spins in the vortex core.