Physics

Imagine that a pair of counter-propagating flows (e.g., current, liquid) move oppositely and exchange associated information, such as voltage potential or pressure via some kind of interactions. In principle, the interaction can lead to a stationary condition that these information are only a function of locations and do not change with time. This stationary condition is not as trivial as that for a pair of co-propagating flows, which is the effective average of them. In this post, we will first focus on the interaction itself and lay down some basic algebra to describe this model, then move to the discussion about quantum Hall effect - a very rare and well-known macroscopic quantum phenomenon and the design of algorithms. We will wrap up this post with implementing algorithms in Python and introducing general usage of Python pacakge. ...

A few days ago, I came across an advert for Sous vide cooker, which is popular for preparing juicy steak. I happened to have an electronic kettle to be replaced. Not very happy with its condition, and a new one was already in my shopping list. Bingo! A natural idea came to me that this kettle can be repurposed to mimic what a Sous vide cooker could do - maintaining a fixed temperature of a body of water for a relatively long time. I knew immediately that this requires a good PID controller just like what I have in a cryostat for stabilizing the sample chamber temperature slightly above the absolute zero. As one may know, the brain of the PID controller is a simple feedback loop governed by three parameters: proportional gain (P), integral gain (I) and derivative gain (D). In practice, in a narrow range of goal temperature, these parameters do not need to be dynamically adapted to a different goal if the external environment is stable. However, it is not guaranteed to always achieve the best stabilization for a wide range of goal temperature for the same set of parameters. That means these parameters also need to be changed if the goal temperature varies. On top of the PID feedback loop, we also need to add another layer of feedback loop to optimize parameters P, I and D. Then the genetic algorithm seems to be useful here for generating the best choice of parameters. Here is a definition for genetic algorithm from MathWorks: ...

Background Landau level In solid-state physics, the famous band theory describes how electrons are distributed favorably over energy and momentum in electronic materials. The states (energy, momentum, spin and etc.) of electrons collectively form an electronic band structure. When subjecting to a magnetic field, these electronic states would shift in energy according to its interactive terms with the field. As this field gets very strong, the interactive term (orbital contribution) becomes dominant and start to form dense bands with narrow energy dispersion (A lot of states have almost the same energy). These bands are also energetically discrete and referred to as “Landau level”. ...