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arXiv · 1803.08122

Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Grégoire Ithier·Saeed Ascroft
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Abstract

We present a non perturbative calculation technique providing the mixed moments of the overlaps between the eigenvectors of two large quantum Hamiltonians: $\hat{H}_0$ and $\hat{H}_0+\hat{W}$, where $\hat{H}_0$ is deterministic and $\hat{W}$ is random. We apply this method to recover the second order moments or Local Density Of States in the case of an arbitrary fixed $\hat{H}_0$ and a Gaussian $\hat{W}$. Then we calculate the fourth order moments of the overlaps in the same setting. Such quantities are crucial for understanding the local dynamics of a large composite quantum system. In this case, $\hat{H}_0$ is the sum of the Hamiltonians of the system subparts and $\hat{W}$ is an interaction term. We test our predictions with numerical simulations.

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Grégoire Ithier, Saeed Ascroft. 2018-03-21. Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors. https://doi.org/10.1088/1751-8121%2Faae800

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