WebGPU-Based 2D Coulomb Gas Simulator: Visualizing Electron Interactions and Log-Gas Hamiltonian

Each dot represents an electron experiencing pairwise Coulomb repulsion with every other electron while being confined by an external potential $Q$.

The energy of a configuration $z_1, \dots, z_n$ is given by the 2D log-gas Hamiltonian $$H(z_1,\ldots,z_n) = -\sum_{i \neq j} \log\lvert z_i - z_j \rvert + n\sum_{j=1}^n Q(z_j).$$

The 2D Coulomb gas is interesting because this type of Hamiltonian shows up in many different places across mathematics / mathematical physics:

Eigenvalues of a random matrix with Gaussian random entries