无序系统的分形行为

本文从大量的实验事实出发，对生长、结构弛豫、动力学行为、光电性能、辐照行为、表面结构、断裂行为七个方面概述了具有随机性质的无序系统中所表现出来的分形行为．说明了分形对于规范和描述这些无序系统中所表现出来的复杂行为的作用，讨论了它的局限性和新近的结果．本文重点地叙述了无序凝聚态材料中的实验结果而未涉及相应的理论部分．     

多标度分形理论及进展

一个分形体的几何特征通常需要用一个多标度分形谱来描述。多标度分形理论建立了分形体的局域标度特性与分形体总体特性的关系。它的物理思想与热力学是类似的。如果已知一个分形体的多标度分形谱,还可以反过来推断其动力学特性。这方面的进展使我们加深了对扩散限制的凝聚过程、完全发达的湍流现象、通向浑纯的若干途径、无序系统等等问题的认识。本文是对上述问题的一篇较为简要的综述。     

微波驱动下超导量子比特与磁振子的相干耦合

实验上展示了钇铁石榴石(YIG)晶体小球中磁振子与超导量子比特的驱动缀饰态之间的相干强耦合,磁振子的加入使得在超导量子比特中形成了双重缀饰态.实验中一个钇铁石榴石晶体小球与一个超导量子比特同时放置在三维谐振腔中,分别通过磁偶极相互作用和电偶极相互作用与谐振腔中的本征场(TE102模式)耦合,并通过腔模作为媒介实现两者之间的有效相干强耦合.给超导量子比特施加一个共振的微波驱动并改变驱动强度,测得耦合系统能级劈裂随驱动强度的变化,并理论上利用粒子-空穴对与玻色场耦合的模型做了计算.在大部分的驱动强度范围内实验结果都与理论计算结果符合得较好,表明驱动下的比特-磁振子耦合系统可以用来模拟粒子-空穴对称对与玻色场的耦合系统.本文使用的混合量子系统为模拟玻色子与费米子的混合系统提供了一个新途径.     

多重耦合振子系统的同步动力学

耦合相振子的同步研究对理解复杂系统自组织协同的涌现具有重要的理论意义.相比于传统耦合振子的两体成对耦合,多重耦合近年来得到广泛的关注.当相振子间的多重耦合机制起主要作用时,系统会涌现一系列去同步突变,这一新颖的动力学特性对理解复杂系统群体动力学提供了重要的理论启示.本文研究了平均场的三重耦合Kuramoto系统的同步动力学,发现了去同步转变具有不可逆性,并利用平均场自洽方法和无序态线性稳定性分析揭示了不可逆去同步突变的动力学机制.进一步研究发现,随着振子自然频率分布半宽度的变化,系统会经历一系列去同步驻波态的转变.在相变临界点,系统在高维相空间会通过鞍结分岔导致同步态失稳而塌缩至稳定的低维不变环面.本文的研究揭示了多重耦合函数作用的振子系统的各种协同态及其相变机制,同时可为理解其他复杂系统(如超网络结构)协同态的动力学转变提供理论借鉴.     

Bi-Pb-Sr-Ca-Cu-O体系的氧空位、局域化和超导电性

本文讨论了热处理过程对浇铸退火方法制备的 Bi-Pb-Sr-Ca-Cu-O 样品的电子输运性质和超导电性的影响.分析了发生非金属-金属(超导)转变的物理过程.指出无论是原子的无序分布,还是氧空位所引起的无规势场增强,都会导致电子局域化增强,使得样品金属性减弱和超导转变温度降低.     

无序效应对1T-TaS_2材料中Mott绝缘相的影响

电子强关联效应使得过渡金属硫化物1T-TaS_2在低温时为Mott绝缘体,而层间堆叠错位及杂质又会引入相当强的无序效应.利用统计动力学平均场理论数值方法研究了无序效应对Mott绝缘相的影响,发现非对角跃迁无序和对角无序效应均不会引起从绝缘体到金属的相变.杂质引入的对角无序达到一定强度后Mott能隙会完全闭合,而堆叠错位引入的非对角跃迁无序不论多强都无法关闭Mott能隙.在半满情况,非对角无序会导致上下Hubard带对称地分别出现一个奇异态,而通过晶格尺寸标度研究证明了这种反常的电子态仍然是Anderson局域态.     

超导理论研究进展

本文概述了超导微观理论研究的最新进展．首先简述了超导微观理论研究的主要成就和重费米子库珀对态的原子表示；然后综述了高温氧化物超导体的微观电子理论和超导机制，其中包括共振价键理论、局域反铁磁交换作用理论、多极化子理论和超导弦理论等．     

一个可能的P波型重费密子超导体——UBe_(13)

在朗道的费密液体理论框架下,我们解释了重费密子超导体UBe_(13)的超导临界温度随压力变化的实验结果。所得结论是:PBe_(13)可能是一个P波型的重费密子超导体。同时也发现由于加压使得系统的f能级与费密能级的相对移动和f电子与导带电子杂化的增加对S波超导有利,而对P波超导不利。     

一类厄尔尼诺-南方涛动耦合振子动力学模型的震荡近似解

研究了一类厄尔尼诺和南方涛动(ENSO)耦合振子动力学模型. 利用奇摄动理论的参数变值法和平均法, 得到了对应ENSO耦合振子模型方程的震荡近似解. 关键词： ENSO振子 奇摄动 近似解     

London磁场的物理机制研究

超导体在旋转过程中会在其内部产生磁场,称为London磁场.目前,包括London理论和G-L理论在内的多种理论都对London磁场的产生机理进行了解释.从本质上,这些理论解释大多认为旋转超导体最外层超导电子运动滞后并由此出现净余电流,而London磁场则是由旋转超导体表面的净余电流产生的.然而,关于旋转超导体最外层超导电子运动滞后的原因,目前仍没有明确的理论解释.本文通过对旋转系中带电粒子,以及旋转超导体中超导电子的贝里相位进行了理论分析,结果表明旋转状态下超导电子的贝里曲率与London磁场具有相同的表达形式,表明London磁场可视为A-B效应的逆效应,也即基于贝里相位的一种宏观量子效应.     

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.     

Influence of superconductivity on the sound propagation in disordered metals

The velocity of sound has been investigated in the disordered metal Nb₂₀Zr₈₀ which contains low energy excitations. From measurements in the superconducting as well as in the normal state the interaction between these excitations and conduction electrons has been studied in detail.     

电—声系统中的费密超导态

基于推广的电－声相互作用模型，考虑到电子的强关联作用，提出了电子算符的玻戈留玻夫近似，导出了声子在电子场中受到的有效作用；证明了波矢相反的纵声子通过交换虚电子能产生一个有效的吸引力，从而构成带有一个电子的声子对。在适当的声子数密度下，形成稳定的费密高温超导态。     

电-声系统中的费密超导态

基于推广的电－声相互作用模型，考虑到电子的强关联作用，提出了电子算符的玻戈留玻夫近似，导出了声子在电子场中受到的有效作用；证明了波矢相反的纵声子通过交换虚电子能产生一个有效的吸引力，从而构成带有一个电子的声子对。在适当的声子数密度下，形成稳定的费密高温超导态。     

Transfer matrices and the glory

The interaction of electrons, photons or other forms of waves with disordered matter gives rise to several complex phenomena including the effect of 'the glory': a peak in the cross section for scattering into the time-reversed state of the incident wave. If the disorder is relatively weak this effect can be described in perturbation theory by summing the so-called 'maximally crossed diagrams'. Transfer matrices, which constitute the major nonperturbative approach to waves in disordered systems, have so far proved incapable of describing the glory. The authors identify the terms in the transfer matrix responsible for this effect. Not only does this remove a deeply unsatisfying incompleteness in transfer matrix theory, but it also provides an economical way of computing diffraction from more complex forms of disorder.     

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk “poor conductors” in which Fermi energy E_F is located in the region of localized states not so far from the Anderson mobility edge E_c. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: ‘critical’ superconductive state formed at E_F = E_c, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E_F still deeper inside a localized band. The ‘critical’ superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap Δ, that is due to many-body correlations and a new “pseudo-gap” energy scale Δ_P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T_c. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to the presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T) ∼ 1/T.Based on these results we propose a new “pseudo-spin” scenario of superconductor-insulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.     

Transfer matrices and the glory

Abstract

The interaction of electrons, photons or other forms of waves with disordered matter gives rise to several complex phenomena including the effect of ‘the glory’: a peak in the cross section for scattering into the time-reversed state of the incident wave. If the disorder is relatively weak this effect can be described in perturbation theory by summing the so-called ‘maximally crossed diagrams’. Transfer matrices, which constitute the major nonperturbative approach to waves in disordered systems, have so far proved incapable of describing the glory. The authors identify the terms in the transfer matrix responsible for this effect. Not only does this remove a deeply unsatisfying incompleteness in transfer matrix theory, but it also provides an economical way of computing diffraction from more complex forms of disorder.