Bibliographic Details
| Title: |
Eigenstate Thermalization Hypothesis for Wigner Matrices. |
| Authors: |
Cipolloni, Giorgio1 (AUTHOR), Erdős, László1 (AUTHOR) lerdos@ist.ac.at, Schröder, Dominik2 (AUTHOR) |
| Superior Title: |
Communications in Mathematical Physics. Dec2021, Vol. 388 Issue 2, p1005-1048. 44p. |
| Subject Terms: |
*RANDOM matrices, *MATRICES (Mathematics), *ERROR probability, *SQUARE root, *HYPOTHESIS |
| Abstract: |
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020). [ABSTRACT FROM AUTHOR] |
|
Copyright of Communications in Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Academic Search Premier |