Dec 12, 2023
Prethermalization for deformed Wigner matrices
Mathphys Analysis Seminar
Date: December 12, 2023 |
4:15 pm –
5:15 pm
Speaker:
Joscha Henheik, ISTA
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Language:
English
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.
