= Two-mode Bose gas on a ring
{c}
{title2=$H=\mathcal E N_1+(U/4\pi)[N(N-1)+2N_0N_1]$}
Project a <bosonic> field on a ring onto angular-momentum modes zero and one. The kinetic level spacing is $\mathcal E=\hbar^2/(2mR^2)$. The contact-interaction <integral> enforces <angular momentum conservation>, leaving two same-mode terms and four mixed terms. The displayed projected <Quantum Hamiltonian> follows by normal ordering. Couplings to discarded modes belong to the full model and can limit the two-mode approximation.
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