Real-space Hamiltonian

The $\alpha$–FPUT chain for $N$ masses with displacement $q_n$ and momentum $p_n$ is

$$H = \sum_{n=1}^{N} \frac{p_n^2}{2} + \frac{1}{2} (q_{n+1}-q_n)^2 + \frac{\alpha}{3} (q_{n+1}-q_n)^3,$$ (13)

with periodic boundary conditions $q_{N+1}=q_1$.

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