Bose Hubbard model

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Introduction

The Bose-Hubbard Model (BHM) was first studied in detail in 1989 by Fisher et al. (need to cite phys rev b article by fisher et al.) They studied a three dimensional Bose gas in several different types of systems, including the most simple case at zero temperature. --> This is just an idea, I havent finished it yet, and dont know if it is necessary so let me know what you guys think about it.

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Hamiltonian

Solving the Hamiltonian

Phase Transition

Experimental Evidence of BHM

First Experiment (Nature Paper)

References