量子布朗运动和原子核裂变

本文研究了在谐振子位势中量子布朗运动与体系粘滞性、温度等参量的关系,观察了体系运动由显示量子行为到完全经典行为的过渡.对由位阱和位垒组成的裂变位势和一般位势情况,通过局域谐振子近似和推广在谐振子位势中的传播子来计算布朗粒子跨越位垒的速率,与经典Fokker-Planck方程(F-P方程)的解相比,它包括了量子效应,因而对量子输运理论的发展具有意义.     

矩形弹子球中的量子谱和经典周期轨道

利用SU(2)相干态的表示,我们构造了二维矩形弹子球中与经典周期轨道对应的波函数.经典周期轨道和量子波函数之间的关系可以通过物理图像清晰的表示出来.另外,利用周期轨道理论,我们计算了二维矩形弹子球体系的量子谱的傅立叶变换ρ(L).变换谱|ρN(L)|2对L图像中的峰可以和粒子在二维矩形腔中运动的经典轨迹的长度相比较.量子谱中的每一条峰正好对应一条经典周期轨道的长度,表明量子力学和经典力学的对应关系.     

探测和操纵量子世界中的个体——2012年诺贝尔物理学奖科学贡献评述

 大家知道, 微观物体通常表现出完全不同于经典物体运动的量子行为, 其根本特征是具有波粒二象性:实物微观粒子会像光波、水波一样, 具有传播、干涉和衍射的波动行为, 这就是所谓的物质德布罗意波;光也会像实物粒子一样具有特定的动量和能量, 与实物粒子碰撞遵守能量-动量守恒定律。     

狄拉克科学贡献中的美学思想

 狄拉克（Ｐ．Ｄｉｒａｃ,１９０２-１９８４）是世界著名的数学物理学家．他的研究工作主要在量子力学的数学和理论两个方面,他最重要的科学贡献是于１９２８年建立了相对论量子力学的狄拉克方程,从而获得了１９３３年诺贝尔物理学奖．其实,狄拉克巨大的科学贡献深受他的美学思想的影响,让我们在此一睹狄拉克科学贡献中的数学美和对称美．一、狄拉克方程──数学美２０世纪２０年代末,量子力学已经建立,用它来研究和处理微观粒子的低速运动问题取得了很大成功．同时,爱因斯坦建立的相对论,虽然能够讨论粒子的高速运动,但在处理微观粒子的波粒二象性上却无能为力．     

引力场中标量粒子波方程的玻姆量子势描述

对于引力场中标量粒子的Klein-Gordon方程,在引入玻姆量子势后,可写出类似于经典粒子的轨道运动方程,继而可表示成重新定义的度规空间中的测地线方程。     

突破原子基石论 人类认识深入到微观世界（下）——一科学发展的人文历程漫话之十二

论述了突破原子基石论、建立经典量子理论之后,人类认识深入到微观世界的曲折过程及思想观念的艰难转变,包括微观粒子二象性的发现、微观粒子运动规律的发现、有关量子力学问题的世纪争论、量子关联性的发现．     

混沌微扰导致的量子退相干

研究了无限深势阱内两个粒子的耦合导致的量子退相干和量子行为趋近于经典混沌运动的过程．当一个粒子的质量减小时,它对另外一个粒子经典混沌扩散的影响逐渐减小．强混沌机理使得轻粒子的作用类似于噪声,从而有效得抑制另外一个粒子的量子相干性．轻粒子的退相干效应随着有效普朗克常数的减小逐渐增强．在这个过程中,另外一个粒子的量子扩散从动力学局域化行为逐渐过渡到经典极限．当有效普朗克常数足够小时。它的量子扩散与经典混沌扩散相符合．该粒子的线性墒随时间演化迅速趋近于饱和值,并且饱和值随着有效普朗克常数减小以指数函数形式从零趋近于l.     

一维均匀势场中含时薛定谔方程的求解

本文详细讨论了一维均匀势场中含时薛定谔方程的求解.求解的思想是以均匀势场中经典粒子的运动作为参考，从经典粒子的运动轨迹出发，构建出量子情形下描述粒子运动的高斯波包形式的演化波函数，进而借助含时薛定谔方程确定波函数的具体形式.在上述思想指导下，推导得出了坐标表象和动量表象下均匀势场内一维粒子的传播子函数.同时，作为比较，狄拉克态矢量符号提供了另一种得到上述传播子函数的途径.     

科学出版社物理类新书推荐

粒子的运动行为依赖于它所受到的力，另一方面，对称性也影响粒子的运动行为．最近美国国家标准与技术研究所（NIST）的Anderlini等提出了一个普遍方法，使用“交换对称”操控超冷中性原子间的相互作用．这可能是指向实际量子计算的重要一步．被光学晶格捕获的超冷原子阵列是存储量子比特的理想物理体系，因为它们与外部环境的随机耦合很弱．     

基于Bloch球面搜索的量子粒子群优化算法

通过分析量子势阱粒子群优化算法的设计过程,提出一种基于Bloch球面搜索的量子粒子群优化算法.首先用基于Bloch球面描述的量子位描述粒子,用泡利矩阵建立旋转轴,用Delta势阱模型计算旋转角度,用量子位在Bloch球面上的绕轴旋转实现搜索.然后用Hadamard门实现粒子变异,以避免早熟收敛.这种旋转可使当前量子位沿着Bloch球面上的大圆逼近目标量子位,从而可加速优化进程.仿真结果表明,该算法的优化能力优于原算法.     

Classical spin and quantum propagation

We consider a classical Brownian motion model of diffusion in two spatial dimensions, where the Brownian particle moves on spiral paths. The classical spin does not change the propagator for the probability density for the position of the particle. However, the subdominant eigenvalues of the classical kernel are simply related to the dominant eigenvalues of the Feynman kernel for an analogous quantum system. The Feynman kernel can be extracted from the classical kernel by coupling to a spin angular momentum of the particle.     

A Discrete, Deterministic Construction of the Phase in Feynman Paths

In the path-integral formulation of quantum mechanics, the phase factor e ^iS(x〈t〉) is associated with every path x〈t〉. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the complex phase was a mathematical device invoked to extract wave behaviour in a particle framework. In this paper we show that the continuous phase itself can have a discrete origin in time reversal and that the propagator can be drawn by a single deterministic path. ¹On leave from Department of Mathematics, Ryerson University, Toronto, Ontario Canada.     

Relativistic quantum mechanics of supersymmetric particles

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge supersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one indludes in the action the boundary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.     

Feynman's approach to quantum mechanics: Trajectories,commutation relations and uncertainty principle

Summary In this paper the meaning of trajectory for a quantum-mechanical particle is discussed, starting from the path integral expression of the propagator. By a direct method the trajectories mostly contributing to the total amplitude are found, but it seems impossible to interpret them as paths in the physical space-time; on the contrary, the position-momentum commutation relations directly follow. Moreover, we show that the Heisenberg uncertaint principle can be obtained from the path integral approach. In order to give a better understanding of the characteristic quantum-mechanical features and of the difference from the classical problems, the diffusion equation for a Brownian particle is considered in the first part of the paper. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

On the thermodynamic origin of the quantum potential

In a new thermodynamic interpretation, the quantum potential is shown to result from the presence of a subtle thermal vacuum energy distributed across the whole domain of an experimental setup. Explicitly, its form is demonstrated to be exactly identical to the heat distribution derived from the defining equation for classical diffusion wave fields. For a single free particle path, this thermal energy does not significantly affect particle motion. However, in between different paths, or at interfaces, the accumulation-depletion law for diffusion waves provides an immediate new understanding of the quantum potential’s main features.     

Classical analog of quantum phase

A modified version of the Feynman relativistic chessboard model (FCM) is investigated in which the paths involved are spirals in space-time. Portions of the paths in which the particle's proper time is reversed are interpreted in terms of antiparticles. With this interpretation the particle-antiparticle field produced by such trajectories provides a classical analog of the phase associated with particle paths in the unmodified FCM. It is shown that in the nonrelativistic limit the resulting kernel is the correct Dirac propagator and that particle-antiparticle symmetry is in this case responsible for quantum interference.