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Showing posts from July, 2021

Coherent and incoherent scattering length of neutron

Neutron scattering length table by NIST [1] When we do calculations relevant to neutron scattering, it is unavoidable that we will come across either coherent, incoherent or total scattering length of elements, which describes the strength of scattering neutrons by different elements, either coherently, incoherently or both. In this article, I will try to uncover the three different types of neutron scattering length, by going through the derivation in details. First, the differential cross section for neutron scattering by a certain structure is given as below -- here we do the derivation for a single-species system so we can derive the relevant scattering length conveniently. \[\frac{d\sigma}{d\Omega} = \sum_{i,j}b_ib_je^{-i\vec{Q}\cdot (\vec{R}_i - \vec{R}_j)}\] where \(i\), \(j\) refers to atoms located at different locations in the structure under beam. In practice, every single \(b_i\), \(b_j\) depends on the corresponding nuclear isotope, spin orientation relative to neutron, nu

Notes on topological physics

Image reproduced from Ref. [5]. In this blog, I will put down my learning notes as reading through the article on topological electrons by A. P. Ramirez and B. Skinner [1]. Basically, I will follow the story flow in Ref. [1] and therefore, first, I will note down the main flow that one can follow to arrive at the notion of topological electrons. Then I will cover the implications of topology and its connection to quantum Hall effect and quantum spin Hall effect. Finally, Weyl semimetal will be covered. It should be pointed that I will not reproduce all the nice discussions presented in Ref. [1]. Rather instead, I will just try to note down those key points or questions that I came across during reading Ref. [1]. First, the topological structure of an geometric object is defined by the Gauss-Bonnet integral, \[\frac{1}{2\pi}\int_S K dA = n\] where \(K\) refers to the curvature at points on surface \(A\). The integral will give us a constant \(n\) which corresponds to the genus (number o

Notes on Ising model

Ernst Ising (Left) and Wilhelm Lenz (Right) - Ising was Lenz's student and the Ising model was claimed (by Ising himself) to be originated by Lenz but named after Ising. Ising model was originally proposed for ferromagnetism and owing to its simplicity in describing the system interaction, it has been widely used in not only describing magnetic systems in theoretical physics area but also in other areas involving similar interaction mechanism. In fact, Ising model can potentially find its position in describing systems involving binary states whereby we have active influence upon each other between neighbors. Here in this blog, I will not try to reproduce those already available beautiful introduction to Ising model - see e.g., Ref. [1-4] and a whole bunch of others one can easily find on Internet. Instead, I will just write down the outline of the problem we are facing once we have the simple Ising model set up for describing the system energy. For example, we always hear people t