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Prethermalization for deformed Wigner matrices

Mathphys Analysis Seminar

Date: Tuesday, December 12, 2023 16:15 - 17:15
Speaker: Joscha Henheik (ISTA)
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series: Mathematics and CS Seminar
Host: Laszlo Erdös

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 $H_\lambda$. 

Based on a joint work with L. Erdös, J. Reker, and V. Riabov. 

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