hello!!I love physics and I study that in Rice University.
what i really doI spend a lot of my time studying wacky equations like \[ \mathcal{H} = -t \sum_{\langle i,j\rangle,\sigma} \bigl( c^{\dagger}_{i\sigma} c_{j\sigma} + c^{\dagger}_{j\sigma} c_{i\sigma} \bigr) % nearest‑neighbour hopping \;+\; U \sum_{i} n_{i\uparrow}\,n_{i\downarrow} % on‑site repulsion \;-\; \mu \sum_{i,\sigma} n_{i\sigma} % chemical potential \] and this equation explains the temperment of electrons in lattice (like the background of this website, haha!). This equation is called the Hubbard Model.
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