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arXiv · 2310.06677

Prethermalization for Deformed Wigner Matrices

László Erdős·Joscha Henheik·Jana Reker·Volodymyr Riabov
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Abstract

We prove that a class of weakly perturbed Hamiltonians of the form $H_\lambda = H_0 + \lambda W$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by $H_\lambda$ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order $\lambda^{-2}$. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix $H_\lambda$.

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László Erdős, Joscha Henheik, Jana Reker, Volodymyr Riabov. 2023-10-10. Prethermalization for Deformed Wigner Matrices. https://doi.org/10.1007/s00023-024-01518-y

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