作为一般知识和技能的力学

学力学分几个层次：专门搞力学（流体或者空气力学），搞物理研究的，搞强梁建筑设计之类的把力学当成工具的，搞一般的自然科学的把力学当成思想的，搞社会科学的把力学当成参考模型、世界观以及思想的。

在这里，我想针对搞物理研究的、搞一般自然科学、搞社会科学的角度，来看一看力学应该优先学哪一些内容。这样的内容应该能够体现牛顿力学的世界观：绝对时间和空间、运动与运动变化原因之间的关系、守恒量、典型力学系统——中心势场、谐振子，然后训练学习者在运用数学结构方面的技能。

  • 先来看学习力学所需要的基础：微积分（一元微积分、不太多的多元微积分，也就是重点包含场的微积分，简单微分方程，矢量运算，线性代数有最好没有也不是大问题）。
  • 再来看牛顿力学，学了这些对于搞社会学的应该已经差不多在技术和思想上都算入门了：
    1. 运动的描述（从实际生活经验到力学概念的抽象过程，这个很重要），运动相关的物理量——位置（空间、坐标系，参考系）、时间、位移、速度、加速度、动量、能量（动能）、角动量
    2. 动力学：力与力的分解、加速度、牛顿第二定律、守恒量、势能，自由落体运动，谐振子，单摆，行星运动，中心势场
    3. 运动坐标系：平动、转动坐标系，运动坐标系下的微分运算，曲线坐标系
    4. 位形空间与相空间，微分方程的解的存在与唯一性
    5. 少体耦合系统，相互作用
  • 接着来看分析力学，对于搞物理的，搞基础自然科学研究的，分析力学是必需的：
    1. 位形空间与相空间，Lagrangian力学，Lagrangian量，作用量，相互作用，最小作用量原理，动力学方程、变分法初步
    2. Hamiltonian力学，Legendre变换，Hamiltonian方程，守恒量，相互作用与保守力
    3. Poisson括号，守恒量，Liouville方程
    4. 谐振子、耦合谐振子、其他耦合系统
  • 最后来看狭义相对论，目前看来只有搞物理的需要它：
    1. 牛顿时空观的问题，实验以及反思，相对性原理
    2. 狭义相对论的时空观，同时的相对性，尺缩钟慢
    3. Minkowski空间初步，空间的线元的长度，四维图，四维物理量
    4. 几何决定动力学，坐标变换不变性、协变性

前面两个部分，在本科一年级课程以内应该是能够完成的。对于数学好、悟性不太差的学生，前面三个应该都能够完成。例如，前4周（20学时）完成数学准备，再用4+2周完成第二部份（其中的两周10学时用在举例以及习题课），再用4周时间教授基本的分析力学，如果可能的话，还能够用两周左右时间讲授相对论。

试一试，有多大的可行性。当然，学生课后要花时间，要主动学习，才行。教材方面，可以参考Feynman’s Lecture on Classical Mechanics，力学概论by方励之，Mechanics by Landau，Classical mechanics：Point particles and relativity by Greiner W.

学习某个学校的校长，为物理也写一个

非常粗糙的作品，一个上午完成的。还要自己慢慢修改，或者大家一起来修改，如果尚足一改话。

我心中的物理学

我知道，
每一天我都在追寻，
追寻我最初的挚爱，
追寻事事物物的来龙去脉。
我知道，
有一天我会明白，
明白一些个为什么，
以及更多的是什么、如何得来。
初次见面，
你表现地很刻板，
总是告诉我是这样是那样；
后来知道，
你是那样的妩媚，
同一颗心却有各种容颜。
有的时候，
埋怨你艰深难懂，
总是充满了结构与符号；
后来才懂得，
你是那样的自然和坦白，
你的语言就是数学与实验。
我曾经以为
时间就像流水任自流，
你让我知道那取决于我跑的是不是够快；
我曾经以为
硬币只能正面或反面，
你让我思索是不是有同时正反面的状态。
我知道，
每一天我都在追寻，
追寻我最初的梦想，
追寻用科学的方法来理解这个世界。
我知道，
每一天我都在享受，
享受为你翻山越岭，
享受每一个山头每一条河流的风采。

我带学生的风格

1、我对学生的课业和研究工作，研究品味方面要求比较高。
2、时间上也要求学生比较投入。
3、在研究内容的选择方面，我给学生比较大的自由。可以慢慢地从我想做的东西里头选择，也可以自己想然后通过与我讨论并得到认可以后拿来做。
4、我会尽量地从idea、实现技术、研究所需知识基础、研究课题的背景和现状的调研等等各个方面给于帮助和指导。
5、我会非常严厉地批评学生，也会非常耐心地给学生从头讲解。
6、只要学生清楚自己在做什么，比较细之地考虑过了自己的选择的结果（当然，我会帮你分析选择的可能后果），我一般都尊重学生的选择。

就算我在严厉批评学生的时候，除了知识积累或者技术实现甚至对这个项目的认可程度方面都差别，学生和我是平等的。学生可以和我争论，我不会伤心、生气。研究工作进展很小的阶段很正常，但是如果我不知道进展小的原因，不知道学生在针对这个情况做什么，就不正常了。我希望学生不要怕找我诉说困难，如果这都怕，要老师干什么？老师就是跟学生一起找到困难到底在什么地方，然后在能够帮忙的时候帮一下的人。在研究工作中起主导或者辅助作用我都愿意。

Jinshan's CV

Jinshan’s Curriculum Vitae

Curriculum Vitae

Jinshan Wu

Department of Systems Science

Beijing Normal University

Tel: +86-10-58807876(O), +86-18610014018(M)

E-mail: Jinshanw@bnu.edu.ca

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  • Education

    • 2011, PH.D. in Condensed Matter Physics, Department of Physics & Astronomy, University of British Columbia (UBC)
    • 2003-2004, one year in a PH.D. program in Simon Fraser University (SFU), and then transferred to UBC
    • 2006, M.Sc. in Condensed Matter Physics, Department of Physics & Astronomy, UBC
    • 2002, M.Sc. in Statistical Physics, Physics Department, Beijing Normal University(BNU)
    • 1999, B.S. in Physics, Department of Physics, BNU

  • Employment

    • 2011-, Associate Professor, Department of Systems Science, BNU, Beijing, China
    • 2004-2011, Teaching Assistant, Department of Physics & Astronomy, UBC
    • 2003-2004, Teaching Assistant, Department of Physics, SFU
    • 2002-2003, Lecturer and Research Associate, Department of Systems Science, BNU

  • Professional experience

    • Associate Professor

      • 2012 Spring, Physics and Mathematics in Studies of Complexity II, graduate course, Department of Systems Science, BNU.
      • 2011 Fall, Physics and Mathematics in Studies of Complexity I, graduate course, Department of Systems Science, BNU.
      • 2011- , Non-equilibrium statistical physics and Quantum transport project, PI, funded partially by National Natural Science Foundation of China.
      • 2011- , Network-based learning strategies of Chinese characters, PI, not yet funded by any agencies.
      • 2012- , Study concept mapping technology and generate collections of concept maps, PI, funded partially by university research fund from BNU.

    • Lecturer

      • 2003, Math Model, undergraduate course, Department of Systems Science, BNU.
      • 2002, Econophysics, a course for graduate students, Department of Systems Science, BNU, 2002,9-2003,1. I designed and established this course from scratch. A review paper ([19] in the publication list) on Econophysics prepared for the class was post on arXiv. Since then many have used it as an introductory material for the subject.

    • Research Associate

      • 2002-2003, under Prof. Zengru Di’s supervision, lead a team working on empirical studies of and modelling weighted complex networks
      • 2002-2003, help Prof. Zengru Di to organize a proposal for National Fund of Natural Science in China, The statistical properties of firm sizes and its theoretical model, funded at 2003,9.

    • Research Assistant

      • 2004-2011, as a graduate student in Prof. Mona Berciu’s group, working on various projects related to quantum transport
      • 1999-2002, as a graduate student (master) in Prof. Zhanru Yang’s group, during the later years of and one year after my graduation (2001-2003), I lead a team working on physical models on complex networks

  • Skills in numerical computation

    • High-performance computational software: BLAS, Lapack, Petsc, Slepc, gsl, xmds
    • Programming language: C, Java, Linux shell script

  • Award

    • University Graduate Fellowship (UGF) from UBC, 2006-2009
    • Graduate Fellowship from SFU, spring 2004
    • Canron Limited – Sidney Hong Memorial Grad Scholarship, Spring 2004
    • Westak International Sales Inc. Grad Scholarship in Expert Systems, Spring 2004
    • Scholarship for Excellent Graduate Students from BNU, 2000
    • Award for excellent undergraduate students from BNU, 1998

  • Research Contribution

    • Quantum Transport

      In my Ph. D. work at UBC I aimed to establish a theoretical framework for finding the non-equilibrium stationary states of quantum systems starting mostly from first principles. Approaches exist for this problem such as the Landauer-Buttiker formula and the non-equilibrium Green’s function method. We decided to use the open-system scenario, which is not widely used because of the difficulty in solving the resulting open-system master equation. Using direct methods, one needs to solve an eigenvalue problem of size 4N where N is the size of the system measured in qubits. We first searched for efficient methods to solve this problem and then applications of this framework on physical models. The following lists several projects I have worked on.

      • Using a BBGKY-like method for solving the open-system master equation [2] the task of solving an eigenvalue problem of size 4N becomes a problem of solving a linear system of size N2 by converting the open-system master equation into linear equations of Green’s functions. The equations of different Green’s functions (single-particle ones, tow-particle ones and so on) are coupled. The cluster expansion, originally used for the equilibrium BBGKY method, is used to truncate the coupled equation. The accuracy of this method is around 2%.
      • The second order form of the BBGKY-like method requires solving a linear system of size N4 but improves accuracy even further. Such a form also gives the two-particle correlated Green’s functions beyond the Hartree-Fock approximation. Manuscript in preparation.
      • A coherent-state representation approach was also explored to solve the above problem of size 4N by simulating a stochastic differential equation with 2N complex variables by converting the open-system master equation into a generalized Fokker-Planck equation. Analytical expression of the non-equilibrium stationary states are derived for some systems. The accuracy of this method is around 6%. Manuscript in preparation.
      • We also found in study of the Kubo formula for open systems [1] that in order to study transport one has to take into account the coupling from the central system to the baths explicitly. In using the usual Kubo formula in transport studies, one assume the central system is a closed system.
      • Using direct methods we studied thermal transport of spin chains[17] and analyzed systems up to N=10. Connections between integrability and anomalous transport, which is widely believed by physicists and has been demonstrated by studies based on the usual Kubo formula, is challenged by our results.

    • Weighted networks

      This series of works started in late 2002 when I was employed as a research associate for Prof. Zengru Di at BNU after I got my M.Sc. Degree in statistical physics from BNU. Many thanks to Prof. Zengru Di, Prof. Yougui Wang and Prof. Zhangang, Han for offering me a position usually requiring a PH.D. Degree. The focus of my research on weighted networks has been the basic statistical features of static weighted networks, their evolution and also some more advanced structure in those networks.

      • Empirical study of weighted networks[11,12]: We collected almost all papers published on Econophysics up to date (back then), compiled a weighted network and studies its basic statistical properties.
      • Evolutionary model for weighted networks [3,7,9]: Inspired by social networks and the above weighted networks of econophysicists, a new model of weighted networks was proposed. It is based on local rules, which means that nodes in the network only need to know limited information about their neighbors and at most their next neighbors. That is in this model a data centers providing global information is not required. We went one step further and conjectured that the well-known mechanism of global preferential attachment (that the richest gets richer while the poorest gets poorer) can be an emergent phenomenon rooted from local rules. We tested and confirmed this conjecture on our own model and several others.

    • Quantum Game Theory[20]

      In physicists’ terminologies, classical games can be regarded as games based on classical objects. The state of the object changes according to players’ choice of strategies. These strategies are described by operators acting on the object to modify its state. The final state of the object determines the payoff for every player. The coin flipping games is a perfect example of this picture. The coin is a classical two-state system, which is denoted by physicists as a mixture state of “heads” and “tails”. Flipping and non-flipping correspond respectively to the Pauli matrixand identity matrix. A natural question then arises of what happens if the classical coin is replaced by a quantum spin.
      I found that the answer is very non-trivial: a probability distribution over the strategy space, which is the description of a general strategy in classical game theory, is no longer capable of describing games with quantum objects. A density matrix over a basis of the strategy space has to be used. The same transition happens from Classical Mechanics to Quantum Mechanics. A probability distribution is replaced by a density matrix, which allows superpositions while the former allows only probability summations.

    • Quantum Foundation[18]

      Partially inspired by the above work on quantum game theory, I was motivated to study the difference between a probability distribution and a density matrix. Can the former be converted to the later equivalently or vice versa? Luckily I found that the same question has been asked and investigated by physicists on the question of validity of hidden variable theory. In a hidden variable theory, there is no superposition principle, but classical probability summations are allowed. In a sense, the hidden variable theory is searching for a map from a density matrix to a classical probability distribution.

      On one hand there is a theorem stating that all convex theories, which includes quantum mechanics, can be embedded into a classical probability theory with constraints (see for example, A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory). On the other hand, Bell’s inequality rules out all local hidden variable theories. The constrained classical theory has to be non-local. Of course many believe that physical theory should be local, but some are still willing to sacrifice locality. I investigated the question of what beyond locality one has to give up in order to have such a classical theory for quantum systems. I found there are many other unacceptable features of the classical theory by explicitly constructing such a theory for systems of one spin half and two spin halfs. Those unwanted features make the theory even harder to understand than the usual quantum mechanics.

  • List of publications

    • 想招两个一年级本科生指导一下

    从物理系和系统科学系找两个新生，最好一边一个，加入我的研究小组。计划用两年时间学习核心课程，两年时间做一些研究工作。在完成普通学生的课程基础上，我会对数学、物理学、计算机、英语课程提出额外的要求，并提供指导。你会花很多其他人玩乐的时间来学习和开展研究工作。这一点你要有心理准备。

    要求：

    1. 对学术研究有浓厚的兴趣
    2. 有毅力，不畏难
    3. 数学、物理学、英语不是很差

    目标：

    1. 完成数学、物理学、计算机科学本科以及硕士研究生阶段的核心课程的学习
    2. 基本的科研训练：学术品味、寻找问题、完成计算、报告学术成果、论文写作
    3. 多学科的兴趣

    待遇：

    1. 考察期间过后，给一定津贴
    2. 完成研究工作的话，按照本组硕士研究生的标准给予奖励

    我的所得：

    1. 更多的学生来完成我的工作。不过这个不重要，其他研究生也可以完成
    2. 试一试在我自己身上管用的学习方法和内容有没有一定的推广价值
    3. 寻找和培养超越我自己的学生，这一点最重要

    关于培养方向的部分细节内容可以参考：工具、课程与学习资料
    关于吴金闪的更多细节可见吴金闪的简历
    关于吴金闪团队的工作的更详细的介绍可见研究计划与进展