Yuanpeng's Blog RSS Feed https://iris2020.net/ In this post, I am going to put down the learning notes for the lecture notes by Prof. David Tong [1]. Direction setup See the figure on Wikipedia page here for all directions involved in the discussion. The classical Hall effect A particle of charge $-e$ in $\mathbf{B}=B\hat{z}$ moves in... Sat, 26 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-26-notes_qhe/ https://iris2020.net/2026-09-26-notes_qhe/ In reciprocal space, some certain combinations of \(hkl\) indices are not observable for certain types of structures. When the missing pattern of \(hkl\) is systematic, we call it systematic absence. For example, for body centered Bravais lattices (oI, tI and cI), only those \((hkl)\) reflections that satisfy the condition \(h... Thu, 24 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-24-systematic_absences/ https://iris2020.net/2026-09-24-systematic_absences/ In this post, I am going to put down the derivation of the Fermi-Dirac distribution and talk about the chemical potential and the Fermi level. Lagrange multiplier To prepare for the derivation, we need to first take a look at the mathematical method for finding optima given constraints, using the... Thu, 24 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-24-fermi_dirac/ https://iris2020.net/2026-09-24-fermi_dirac/ Recall the Bloch’s theorem Some basic results of the Bloch’s theorem is reproduced here. For more detailed discussion, refer to my earlier post here. The Bloch function, \[\psi_{n\mathbf{k}}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} u_{n\mathbf{k}}(\mathbf{r})\] where $u_{n\mathbf{k}}(\mathbf{r})$ is periodic with the lattice periodicity. Substituting into the full Schrödinger equation $H\psi_{n\mathbf{k}} = E_{n\mathbf{k}}\psi_{n\mathbf{k}}$ gives an... Thu, 24 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-24-berry_ahe/ https://iris2020.net/2026-09-24-berry_ahe/ In solid states physics, a very fundamental building block for explaining and understanding all sorts of phenomena is the band structure. What is it? In quantum mechanics, we know that the energy levels of atoms are not continuous – they come in discrete levels. Usually when we draw atomic energy... Mon, 21 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-21-bloch_band/ https://iris2020.net/2026-09-21-bloch_band/ We all know different colors in the sun light will be separated by a prism due to the different refraction index of light with different wavelength. Saying that, we basically mean that the refraction index \(n\) is a function of the wavelength \(\lambda\). The specific functional relation depends on the... Sun, 20 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-20-dispersion/ https://iris2020.net/2026-09-20-dispersion/ \(R3m\) Diagram Let’s continue the discussion on some (random) topics about crystallography, and this time, I will start with looking at the diagram for the space group \(R3m\). Meaning carried by those symbols in the diagram are well explained in Refs. [1, 2] and I won’t reproduce them here. I... Fri, 18 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-18-crystallography_r2/ https://iris2020.net/2026-09-18-crystallography_r2/ This series of posts are not meant to be a systematic note about a specific topic. It’s a collection of learning notes on a few basic topics on crystallography and may come in a sort of random order, which may seem a bit messy at a first (second, or maybe... Thu, 17 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-17-crystallography_r1/ https://iris2020.net/2026-09-17-crystallography_r1/ In a previous post about enantiomorph, I mentioned the affine space in which we locate ourselves for talking about the space groups. Staying in the affine space, we have 230 space groups in total, and if we do not care about the handedness, we have 219 inequivalent space groups in... Tue, 15 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-15-abstract_algebra/ https://iris2020.net/2026-09-15-abstract_algebra/ Mirror Translation & Rotation Pause Reset Enantiomorph An enantiomorph is a mirrored structure of an original structure – it can be obtained via reflection as shown in the animation above. After the reflection, all the basic metrics (distance and angle) are kept – the two structures are basically the same... Mon, 14 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-14-enantiomorph/ https://iris2020.net/2026-09-14-enantiomorph/ Image generated with Gemini with the prompt ‘generate an abstract image for my blog post about optimization methods like Newton method, Gauss-Newton, Levenberg-Marquardt, etc,. use the Ghibli style’. A summary of optimization methods will be presented in the current post, giving an idea about what methods we have, their categories... Tue, 01 Sep 2026 00:00:00 -0400 https://iris2020.net/2026-09-01-optimization/ https://iris2020.net/2026-09-01-optimization/ Image generated with Gemini with the prompt ‘generate an abstract image for demo of decision tree pictorially. use the Ghibli style’. Introduction A decision tree is composed of various nodes branching from the top to the bottom, forming a tree-like structure. Each node is a preset criterion based on which... Fri, 28 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-28-decision_tree/ https://iris2020.net/2026-08-28-decision_tree/ Image generated with Gemini with the prompt ‘generate an abstract image for demo of Poisson distribution pictorially. use the Ghibli style’. Introduction Poisson distribution is usually used to describe the distribution of independent discrete events happening in a constant rate. For example, in neutron scattering experiments, detectors record the events... Thu, 27 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-27-poisson_distribution/ https://iris2020.net/2026-08-27-poisson_distribution/ Introduction In this post, I am going to put down some notes on a very nice paper by Prof. Z. T. Chen from UT Austin. The paper implements a physics model guided Bayesian optimization for spectroscopy experiment steering [1]. As a high-level summary, the backbone of the paper is as... Wed, 26 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-26-bo_adv/ https://iris2020.net/2026-08-26-bo_adv/ Image generated with Gemini with the prompt ‘generate an image for me as an interesting head image in my Bayesian optimization post. when people see the image, they know the post is talking about the BO. but it should not be an illustrative image showing details of BO. just an... Wed, 19 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-19-gp_bo/ https://iris2020.net/2026-08-19-gp_bo/ This post is part-4 of the 4-parts full story about the Langevin dynamics. All references are presented in the current part. Part IX – Static Targets: The Bridge to Generative Modelling Everything to this point has been physics: given a potential \(U\), sample its Boltzmann distribution. Generative modelling inverts the... Mon, 17 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-17-langevin_dynamics_4/ https://iris2020.net/2026-08-17-langevin_dynamics_4/ This post is part-3 of the 4-parts full story about the Langevin dynamics. All references will be presented in part-4. Part VII – The Overdamped (Smoluchowski) Limit 7.1 The physical regime Two timescales are present in the Langevin system: Timescale Symbol Meaning Momentum relaxation \(\tau_p = 1/\gamma = m/\zeta\) time... Sun, 16 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-16-langevin_dynamics_3/ https://iris2020.net/2026-08-16-langevin_dynamics_3/ This post is part-2 of the 4-parts full story about the Langevin dynamics. All references will be presented in part-4. Part IV – The Fluctuation–Dissipation Relation The task of this part is to determine the relationship between the two coefficients \(\gamma\) and \(\sigma\) left undetermined in (2.1). Two logically distinct... Sat, 15 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-15-langevin_dynamics_2/ https://iris2020.net/2026-08-15-langevin_dynamics_2/ This post is part-1 of the 4-parts full story about the Langevin dynamics. All references will be presented in part-4. 0. Scope, prerequisites, and how to read this This document develops Langevin dynamics from first principles and follows a single thread all the way from classical statistical mechanics to the... Thu, 13 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-13-langevin_dynamics_1/ https://iris2020.net/2026-08-13-langevin_dynamics_1/ In one of my earlier posts [1], several typical sampling algorithms were briefly discussed, such as the direct inverse sampling, rejection sampling and Markov Chain Monte Carlo (MCMC) sampling. The direct inverse sampling requires analytical form of the distribution function and reversability. For suitable 1D distribution function, it can be... Thu, 13 Aug 2026 00:00:00 -0400 https://iris2020.net/2026-08-13-gibbs_sampling/ https://iris2020.net/2026-08-13-gibbs_sampling/