20.500.12556/RUL-175283 Microcanonical free cumulants in lattice systems Recently, the full version of the eigenstate thermalization hypothesis (ETH) has been systematized using free probability. In this paper, we present a detailed discussion of the free-cumulants approach to many-body dynamics within the microcanonical ensemble. Differences between the latter and canonical averages are known to manifest in the time-dependent fluctuations of extensive operators. Thus, the microcanonical ensemble is essential to extend the application of free probability to the broad class of extensive observables. We numerically demonstrate the validity of our approach in a nonintegrable spin-chain Hamiltonian for extensive observables at finite-energy density. Our results confirm the full ETH properties, specifically the suppression of crossing contributions and the factorization of noncrossing ones, thus demonstrating that the microcanonical free cumulants encode ETH smooth correlations for both local and extensive observables. quantum statistical mechanics spin chains eigenstate thermalization random matrix theory kvantna statistična mehanika kvantni kaos spinske verige termalizacija lastnih stanj teorija naključnih matrik true false true Angleški jezik Slovenski jezik Članek v reviji 2025-10-23 10:49:19 2025-10-23 10:49:20 2025-12-09 03:54:44 0000-00-00 00:00:00 2025 0 0 Str. 054303-1-054303-16 iss. 5 Vol. 111 2025 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 536.9 2469-9950 10.1103/PhysRevB.111.054303 254422787 2409.01404v1.pdf 2409.01404v1.pdf 1 F286C252C32D463D447BC306ABC8D4D4 3c3dcd42815b6fadc4d8b40d262f20743e98b01aa72316c733786f860a73281f c3b25370-afed-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220719 https://journals.aps.org/prb/abstract/10.1103/PhysRevB.111.054303 0 cfb0888f-afed-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220720 Fakulteta za matematiko in fiziko 0 0 0