Antiferromagnetism For a bipartite lattice with $J_{ij}\geq 0$, one can assume a Néel state that is the fully polarized ground state with the opposite directions for the two sublattices. It is wri...

Heisenberg model The Hamiltonian of the Heisenberg model is represented as: [\begin{equation} H = \sum\limits_{\braket{ij}}J_{ij}\mathbf{S}{i}\cdot\mathbf{S}{j} \end{equation}] where the sum $i$...

Spin-orbit coupling Spin-orbit coupling (SOC) is a relativistic effect originating from the relative motion between the valence electron and the nucleus. If an electron is in a fixed inertial fram...

Using TradingAgents with Local LLM This note is a comprehensive guide for setting up the TradingAgents framework with a local LLM engine inside a Docker environment on an Apple Silicon chip. Docke...

Long story short,launchd is the framework to automate background jobs on the Mac OS system. It is analogous to systemd in Linux. This requires a plist file that encodes what Mac should do. The plis...

Signing Hash Management One should remember that the hash keys for signing in the project use for three different purposes: 1. Quality Assurance One uses the keystore for the local release deplo...

How to use ADB? ADB is an abbreviation of Android Debug Bridge. This tool allows us to control an Android phone using our local computer. First, connect the device to the PC. Then turn on the deve...

The following notes assume you are using an M1 Mac system. Install the Docker image. First, we must see if there’s an Ubuntu image in the Docker container: $ docker search ubuntu Then we downl...

Topology To define the neighborhood, one should discuss an open set. An open set is a set of points between an open interval in that they exclude their boundary points. For example, the open set $...

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