当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋—１／２算符理论考察了Ｉ＝１的核四极共振自旋系统在其能级间隔较小时对１—２个脉冲的响应．由于核四极相互作用表象中的射频场与核自旋的相互作用（Ｈｎ）包含时间．因而用Ｄｙｓｏｎ时序算符来计算密度算符在Ｈｎ作用下的演化．     

当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋-1/2算符理论考察了I=1的核四极共振自旋系统在其能级间隔较小时对1-2个脉冲的响应.由于核四极相互作用表象中的射频场与核自旋的相互作用(H_rf)包含时间,因而用Dyson时序算符来计算密度算符在H_rf作用下的演化.     

两个力学量算符具有共同本征态系的条件

量子力学是人们了解微观世界的一门重要的课程.在量子力学中,由于任何实物体都具有波粒二象性,必须用算符来表示力学量,因此算符理论显得尤为重要.在研究多个算符时,有一个非常重要的定理:两个力学量算符能够具有共同本征函数系的充分必要条件是这两个个力学量算符能够互相对易.本文分析了在使用该定理时可能存在的一些问题,并对这些问题进行了澄清.     

“库柏对”的诞生

基于史料,阐述了库柏对产生的经过     

哈密顿算符的对角化与能量本征值问题的代数解法

提出了将哈密顿算符对角化的一种方法.围绕一维谐振子讨论了如何将哈密顿算符对角化、引进的是玻色算符还是费米算符的问题,并分析了能量量子化的原因及能量子与声子的区别.     

非对易相空间中角动量的分裂

非对易空间效应是一种在弦尺度下出现的物理效应. 本文首先介绍了在Schwinger表象中角动量的3个分量用产生--消灭算符的表示形式, 接着讨论了非对易相空间的量子力学代数; 然后用对易空间谐振子的产生-消灭算符表示出了在非对易情况下的角动量; 最后讨论了非对易相空间中角动量的分裂.     

两体组合坐标表象的建立、性质及应用

为了研究具有相互作用势和运动耦合的两个非全同的量子谐振子体系的动力学问题,利用有序算符乘积内的积分技术,建立了一种两粒子体系的组合坐标新表象|η₁,η₂〉,构造了一个双模压缩算符U并分析了其压缩特性. 应用组合坐标新表象严格求解了具有相互作用势和运动耦合的两个非全同的量子谐振子体系的动力学问题. 这为研究复杂耦合量子谐振子体系提供了一个有效途径. 关键词： 有序算符乘积内的积分技术 组合坐标表象 双模压缩算符 幺正矩阵     

非对易相空间及其狄拉克粒子电磁场中的运动

近年来,有关非对易空间的各种物理问题成为诸多学者研究的热点,并在量子力学、量子场论、量子电动力学、凝聚态物理、天体物理等各领域中被广泛探讨.本文通过非对易空间里电磁场中狄拉克粒子的哈密顿量,推导出速度算符和所受到的力算符的表达式,利用Bopp变换方法给出了电磁场作用下的狄拉克粒子在非对易空间和非对易相空间中的哈密顿量,从而推导出了速度算符和力算符的表达式,其中均包含因非对易引起的修正项.在此基础上进一步分析得出,非对易效应对狄拉克粒子的速度算符和所受到的力算符有一定的影响,但动量-动量算符的非对易性对粒子的速度算符没有影响.     

电子自旋是角动量的讨论

从施特恩-盖拉赫实验测量的结果电子自旋只有两种取值出发,在不引入自旋算符的具体矩阵表示的情况下,利用矩阵求迹,导出自旋算符和轨道角动量算符满足完全相同的对易关系,从而说明自旋与轨道角动量同类,属于角动量.区别于历史上和国内外量子力学教材中直接将自旋归为角动量,本文尝试用"物以类聚"的逻辑对自旋是角动量进行讨论.     

外场与介观约瑟夫森结相互作用的不变本征算符法研究

本文首先详细介绍了场与介观约瑟夫森结相互作用系统的哈密顿量,进一步讨论了系统的量子化方案,然后简要介绍了不变本征算符法及其基本应用.在此基础上,用不变本征算符法求得外场与介观约瑟夫森结相互作用系统的能级间隔.     

Towards a theory of superconductivity based on collective Cooper pairs

Superconductivity could be seen as a Bose-Einstein condensation (BEC) of Cooper pairs. However, the creation and annihilation operators of Cooper pairs do not satisfy the bosonic commutation relations and then, the mentioned viewpoint has a weakness in its foundation. In this work, we introduce the concept of collective Cooper pairs (CCP) as linear combinations of Cooper pairs and prove their bosonic nature at the dilute limit. This bosonic nature is given rise from their diffuse character on the Cooper pairs, which permits the accumulation of many collective pairs at a single quantum state. Moreover, the superconducting ground state proposed by Bardeen, Cooper and Schrieffer (BCS) can be written in terms of these collective Cooper pairs, which means that the BCS theory is consistent with a possible BEC theory of superconductivity based on collective Cooper pairs. Finally, we calculate the energy spectra and the BEC critical temperature of CCP.     

Bosonic nature of collective Cooper pairs

Superconductivity is not considered as a Bose-Einstein condensation, because the creation and annihilation operators of Cooper pairs do not satisfy bosonic commutation relations. However, collective pairs can be constructed by a linear combination of Cooper pairs and we demonstrate in this Letter that these collective Cooper pairs have bosonic nature. In addition, the Bardeen-Cooper-Schrieffer (BCS) superconducting ground state can be built by means of these pairs and in consequence, could be treated as a Bose-Einstein condensate.     

Superconducting plate in a transverse magnetic field: New state

A model is proposed for describing Cooper pairs near the transition (in temperature and magnetic field) point when their spacing is larger than their size. The essence of the model is as follows: the Ginzburg-Landau functional is written in operator form in terms of field operators of the Bose type so that the average value of the density operator gives the concentration of Cooper pairs, and the same Ginzburg-Landau expression is obtained for the Bose condensate. The model is applied to a superconducting plate with a thickness smaller than the size of a pair in a transverse magnetic field near its upper critical value H _c2. A new state is discovered that is energetically more advantageous in a certain interval in the vicinity of the transition point as compared to the Abrikosov vortex state. The wavefunction of the system in this state is of the type of the Laughlin function used in the fractional quantum Hall effect (naturally, as applied to Cooper pairs as Bose particles in our case) and corresponds to a homogeneous incompressible fluid. The energy of this state is proportional to the first power of quantity (1 ? H/H _c2) in contrast to the energy of the vortex state containing the square of this quantity. The interval of the existence of the new state is the larger, the dirtier the sample.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

Electromagnetic Meissner effect in spin-one color superconductors

It is shown that color-superconducting quark matter, where quarks of the same flavor form Cooper pairs with spin one, exhibits an electromagnetic Meissner effect. This is in contrast to spin-zero color superconductors where Cooper pairs consist of quarks with different flavors.     

Cooper Molecules: Second Pairing of Cooper Pairs in Gapless Superconductor CeCoIn_5

We establish a quantum field theory of phase transitions in gapless superconductor CeCoIn5.It is found that uniform Cooper pair gases with pure gradient interactions with negative coefficient can undergo a BardeenCooper-Schrieffer (BCS) condensation below a critical temperature.In the BCS condensation state,bare Cooper pairs with opposite wave vectors are bound into Cooper molecules,and uncoupled bare Cooper pairs are transformed into a new kind of quasiparticle,i.e.,the dressed particles.The Cooper molecule s.ystem is a condensate or a superfluid,and the dressed particle s.ystem is a normal fluid.The critical temperature is derived anal.yticall.y.The critical temperature of the superconductor CeCoIn5 is obtained to be T_c = 2.289 K,which approaches the experimental data.The transition from the BCS condensation state to the normal state is a first-order phase transition.     

电-声超导电性的对称理论

利用新的库珀对平均汤近似，导出了电－声系统中声子－库珀对有效作用，证明了声子通过交换虚的库珀对能够产生一个有效的吸引力，导致两动量相反的声子配对并构成稳定的声超导态。发现电子超导态与声子超导态的直积能构成稳定的电－声对称的高温超导基态。在声子－库珀对弱耦合极限下，基态对称破缺成为传统的ＢＣＳ基态。     

电—声超导电性的对称理论

利用新的库珀对平均汤近似，导出了电－声系统中声子－库珀对有效作用，证明了声子通过交换虚的库珀对能够产生一个有效的吸引力，导致两动量相反的声子配对并构成稳定的声超导态。发现电子超导态与声子超导态的直积能构成稳定的电－声对称的高温超导基态。在声子－库珀对弱耦合极限下，基态对称破缺成为传统的ＢＣＳ基态。     

Long-range superharmonic Josephson current

We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an odd number of Cooper pairs cannot have a long-range propagation when there is only one spin-active region. When the temperature is much lower than the Thouless energy, the coherent transport of two Cooper pairs becomes the dominant process and the superharmonic current-phase relation is obtained (I ∝ sin2?).     

Final-state effects in the radio frequency spectrum of strongly interacting fermions

We model the impact of final-state interactions on the radio frequency spectrum of a strongly interacting two-component superfluid Fermi gas. In addition to a broad asymmetric peak coming from the breakup of Cooper pairs, we find that, for appropriate parameters, one can observe a sharp symmetric "bound-bound" spectral line coming from the conversion of Cooper pairs in one channel to pairs or molecules in another.