# Form and effect of the intrinsic Hamiltonian on the IBM machines

I want to understand the form of the intrinsic Hamiltonian of the IBM machines, such as ibmq_16_melbourne, and how this affects the data I get out when waiting using identity gates.

From the ZZ-characterisation tutorial in the documentation, it seems like the general form of the intrinsic Hamiltonian is $$\mathcal{H} = \sum_i^N \frac{2\pi\nu_i}{2} (1-\sigma_i^z)+\sum_{ij}^N\frac{\xi_{ij}}{4}\left(1-\sigma_i^z\right)\left(1-\sigma_j^z\right),$$ with sums in theory over all $$N$$ qubits. Here $$\nu_i\approx 5\,\text{GHz}$$ and $$\xi_{ij}$$ seem to take values up to $$\sim 100\,\text{kHz}$$, but only significantly above $$0$$ for nearest neighbours. Is this correctly understood?

Now, if I prepare an initial state $$\frac{1}{\sqrt2}\left(|0\rangle +|1\rangle\right)\otimes|0\rangle^{N-1}$$ I do not see oscillations with a frequency anywhere near $$5\,\text{GHz}$$, but rather something closer to $$100\,\text{kHz}$$. Does this mean that the measurements are being taken in the co-moving frame with frequencies for each qubit being $$\nu_i$$? If so, why do I have these residual oscillations?