大摆角单摆“周期”变化的解析解及其实验应用

大摆角单摆实验由于忽略空气阻尼带来周期测量的系统误差.基于弱阻尼大摆角单摆的运动方程,推导了累计"周期"随摆次变化的解析公式,分析了"周期"随摆次减小的基本规律.结合实验数据分析,验证了将其用于大摆角单摆实验进行系统误差修正,从而通过累计测量减小随机误差的可行性.     

介观电路中量子纠缠的经典对应

从量子力学诞生日起,它的经典对应(或类比)一直是物理学家关心的话题.本文以介观电路量子化的框架中,带有互感的两个介观电容-电感(LC)电路为例,首次讨论了量子纠缠的经典类比(或对应)问题.先用有序算符内的积分理论证明其互感是产生量子纠缠的源头;再推导出求解特征频率的公式,就发现它与一个经典系统的小振动频率的表达式有相似之处,该经典系统组成如下:两个墙壁各连一个相同的弹簧,两个弹簧之间接着一个滑动小车可以在光滑的桌面上运动,小车挂有一根单摆.用分析力学求此系统的小振动频率,发现与上述介观电路的特征频率形式类似,单摆的摆动会造成小车来回振动,摆、小车和弹簧的互相牵制效应反映了小车和摆的"纠缠".     

用单摆测重力加速度的改进

1 实验概况 由单摆振动周期公式可得,所在地重力加速度由公式 实验中单摆不可能完全符合单摆模型的要求.为了减小各种不符合因素对单摆周期的影响,常规的学生实验总要求轻质细绳的长度超过1m.球形重物(摆球)直径小于1cm,摆角小于5°.     

用单摆法测重力加速度实验的改进

用单摆测重力加速度是大学和中学物理课的必做实验，实验装置简单，方法容易掌握，十分有助于提高学生分析、解决问题的能力．但由于多种原因使这个实验误差较大，进度缓慢，若对原有装置稍加变化，在单摆立柱和摆球之间固定一小图板，在图板上贴一张白纸，如图，就能有效的减小以下三方面的误差，并加快实验速度．实验装置图1．当摆球在空间摆动时，原单摆装置要求用目测观察摆球在一个平面内摆动就认为是单摆运动．但这种观察无显著的参照标准，极有可能把锥摆视为单摆，造成实验误差．若以图中贴纸图板表面为参照面，每次调节摆长后再调…     

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.     

单摆系统的振动研究

通过求解变张力弦振动微分方程的边值问题,给出摆线与摆球的质量比为任意值时单摆系统运动的一般解和本征频率满足的方程.利用该方程求得高精度的单摆系统周期数值解,特别是拟合出单摆系统作基频振动时一个范围大、精度高的周期近似公式.同时将理论与实验进行比较,结果二者相符.     

利用 Tracker 软件分析单摆测定重力加速度

Tracker 软件是一种广泛使用的视频分析软件,通过分析物理实验视频,追踪研究对象的运动轨迹,以 简洁、高效的数据分析手段揭示物理现象背后所隐藏的物理规律. 利用 Tracker 软件分析了单摆测定重力加速度的 实验视频,通过自动追踪摆球运动的轨迹,精确测得了单摆运动的周期和重力加速度     

单摆周期公式的来源和推导

本文介绍了单摆周期公式发现的历史,并提供了一种较简单的、接近惠更斯时代知识背景的推导方法. 一 问题的缘起 我们在上《单摆》这一节课,讲到《单摆振动的周期》这部分时,一般用实验演示单摆振动的周期与振幅、摆长、摆球的质量、重力加速度的关系.     

非惯性系中单摆周期研究

 高中物理“单摆”的考查重点是单摆周期的计算,其中尤以在匀变速运动系统中的单摆周期的计算为难点。传统方法是求出单摆的等效重力加速度ｇ′,代入周期公式Ｔ=2πｌ/ｇ′即可。而等效重力加速度ｇ′的求法是:先确定单摆在系统中的平衡位置,然后求出平衡位置时摆线对摆球的拉力Ｔ′,最后确定ｇ′,ｇ′=Ｔ′/ｍ,ｍ为摆球质量。上述方法能有效地解决问题,但其物理意义不明显。本文拟从动力学角度出发,在非惯性系中讨论此问题。首先就一般情况,得出一个普遍适用的公式,然后对几种特殊情况加以分析。1.沿倾角对α的斜面匀加速上滑的非惯性系实例:放在沿斜面匀加速上滑的小车中的单摆。     

基于电磁感应原理的单摆法测量重力加速度

本文将单摆法与电磁感应原理相结合,用永磁球体作为摆球,并且在其正下方放置多匝线圈.当摆球做简谐运动时,线圈内部磁通量对应地发生周期性变化,从而产生周期性的感应电动势.使用滤波器模块过滤噪声,并利用示波器采集周期性信号.通过判读电动势信号即可准确获取单摆的周期信息.进一步通过改变摆球和线圈之间的相对高度衡量电磁阻尼对于测量的影响,发现测量的周期与相对高度无关,说明电磁阻尼是可以忽略的,这与半定量分析结果是一致的.本文测量的重力加速度实验值与本地参考值有很好的一致性.     

Nonlocality in the Expanding Infinite Well

According to D. Bohm's interpretation of quantum mechanics, a particle always has a well-defined spatial trajectory. A change in boundary conditions can nonlocally change that trajectory. In this note we point out a striking instance of this phenomenon that is easy to understand qualitatively.     

Bringing quantum mechanics to life: from Schrödinger’s cat to Schrödinger’s microbe

The question whether quantum mechanics is complete and the nature of the transition between quantum mechanics and classical mechanics have intrigued physicists for decades. There have been many experimental breakthroughs in creating larger and larger quantum superposition and entangled states since Erwin Schrödinger proposed his famous thought experiment of putting a cat in a superposition of both alive and dead states in 1935. Remarkably, recent developments in quantum optomechanics and electromechanics may lead to the realisation of quantum superposition of living microbes soon. Recent evidence also suggests that quantum coherence may play an important role in several biological processes. In this review, we first give a brief introduction to basic concepts in quantum mechanics and the Schrödinger’s cat thought experiment. We then review developments in creating quantum superposition and entangled states and the realisation of quantum teleportation. Non-trivial quantum effects in photosynthetic light harvesting and avian magnetoreception are also discussed. At last, we review recent proposals to realise quantum superposition, entanglement and state teleportation of micro-organisms, such as viruses and bacteria.     

量子信息讲座第一讲 量子计算机

量子力学和计算机理论，这两个看起来互不相关的领域，其结合却产生了一门富于成效的学科：量子计算机．文章介绍了量子计算机的基本概念和历史背景，它相对于经典计算机的优越性，它的构造和实验方案，以及实现量子计算的困难及其克服途径，最后展望了量子计算机的发展前景     

A Spatial Domain Quantum Watermarking Scheme

This paper presents a spatial domain quantum watermarking scheme. For a quantum watermarking scheme, a feasible quantum circuit is a key to achieve it. This paper gives a feasible quantum circuit for the presented scheme. In order to give the quantum circuit, a new quantum multi-control rotation gate, which can be achieved with quantum basic gates, is designed. With this quantum circuit, our scheme can arbitrarily control the embedding position of watermark images on carrier images with the aid of auxiliary qubits. Besides reversely acting the given quantum circuit, the paper gives another watermark extracting algorithm based on quantum measurements. Moreover, this paper also gives a new quantum image scrambling method and its quantum circuit. Differ from other quantum watermarking schemes, all given quantum circuits can be implemented with basic quantum gates. Moreover, the scheme is a spatial domain watermarking scheme, and is not based on any transform algorithm on quantum images. Meanwhile, it can make sure the watermark be secure even though the watermark has been found. With the given quantum circuit, this paper implements simulation experiments for the presented scheme. The experimental result shows that the scheme does well in the visual quality and the embedding capacity.     

Quantum deleting and cloning in a pseudo-unitary system

In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum deleting and cloning in a pseudo-unitary system. We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system. By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian, we show that it is possible to delete and clone a class of two different and nonorthogonal states, and it can be generalized to arbitrary two different and nonorthogonal pure qubit states. Furthermore, state discrimination, which is strongly related to quantum no-cloning theorem, is also discussed. Last but not least, we simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection, and obtain the success probability of simulations. Pseudo-unitary operators are implemented with a limited efficiency due to the post-selections. Thus, the success probabilities of deleting and cloning in the simulation by conventional quantum mechanics are less than unity, which maintain the quantum no-deleting and no-cloning theorems.     

Creation of quantum correlations via the initial classical-mixed states

Using the pseudomode method, we theoretically analyze the creation of quantum correlations between two two-level dipole-dipole interacting atoms coupled with a common structured reservoir with different coupling strengths. Considering certain classes of initial separable-mixed states, we demonstrate that the sudden birth of atomic entanglement as well as the generation of stationary quantum correlations occur. Our results also suggest a possible way to control the occurrence time of entanglement sudden birth and the stationary value of quantum correlations by modifying the initial conditions of states, the dipole-dipole interaction, and the relative coupling strength. These results are helpful for the experimental engineering of entanglement and quantum correlations.     

量子通信

量子通信是经典通信和量子力学相结合的一门新兴交叉学科。文章综述了量子通信领域的研究进展，既包括人们所熟知的量子隐形传态、密集编码和量子密码学，也包括刚刚兴起但却有巨大潜力的量子通信复杂度和远程量子通信等领域。文章介绍了量子通信的基本理论框架，同时也涉及了这个领域最新的实验研究的进展。     

Time-Symmetric Quantum Mechanics

A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P₀ is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum mechanics with an important fundamental symmetry.     

The physics of 2≠1+1

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as “ghost” interference and “ghost” imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 ≠ 1 + 1.