信息动态

振动力学相关课程,是很多工科专业本科和研究生的重要课程,调研国内外主要大学相关课程设置及教材采用和推荐情况,对课程教学和教材改革有重要的参考价值. 本文对国内、美国若干所主要工科院校振动力学相关课程设置的专业、学时数以及采用或参考的教材进行了调研. 参照国内从早期到目前为止的大部分教材,并对照美国几本使用较广的教材,全面总结分析了国内振动力学相关教材的发展历程、编写特点. 最后,对提高振动力学教材编写水平、非力学类工科专业的振动课程设置及教学提出了几点建议.     

Mottness,phase string,and high-Tc superconductivity

It is a great discovery in physics of the twentieth century that the elementary particles in nature are dictated by gauge forces, characterized by a nonintegrable phase factor that an elementary particle of charge $q$ acquires from $A$ to $B$ points: $P \exp \left( \text{i} \frac q {\hbar c}\int_A^B A_{\mu}\text{d} x^{\mu}\right),$ where $A_{\mu}$ is the gauge potential and $P$ stands for path ordering. In a many-body system of strongly correlated electrons, if the so-called Mott gap is opened up by interaction, the corresponding Hilbert space will be fundamentally changed. A novel nonintegrable phase factor known as phase-string will appear and replace the conventional Fermi statistics to dictate the low-lying physics. Protected by the Mott gap, which is clearly identified in the high-$T_{\rm c}$ cuprate with a magnitude $> 1.5$ eV, such a singular phase factor can enforce a fractionalization of the electrons, leading to a dual world of exotic elementary particles with a topological gauge structure. A non-Fermi-liquid "parent" state will emerge, in which the gapless Landau quasiparticle is only partially robust around the so-called Fermi arc regions, while the main dynamics are dominated by two types of gapped spinons. Antiferromagnetism, superconductivity, and a Fermi liquid with full Fermi surface can be regarded as the low-temperature instabilities of this new parent state. Both numerics and experiments provide direct evidence for such an emergent physics of the Mottness, which lies in the core of a high-$T_{\rm c}$ superconducting mechanism.     

由机械能守恒给出第二类Lagrange方程的探究

保守系统的运动微分方程,可以使用第二类Lagrange方程列写,从Langrage 方程也可以推导出保守系统的机械能守恒. 有老师提到,曾有学生在作业中用机械能守恒给出正确的Lagrange 方程. 本文探讨这种做法的可行性,并针对某些特殊情况给出了由机械能守恒得到Lagrange 方程的具体步骤.