Emergence of Fermi's Golden Rule
Abstract
Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a {\it continuum} of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing; this question arises in a number of recently investigated many-body systems. For different symmetry classes, we analytically and/or numerically calculate the universal crossovers in the average decay of the initial state as the level spacing is varied, with the Golden Rule emerging in the limit of a continuum. Among the corrections to the exponential decay of the initial state given by FGR is the appearance of the spectral form factor in the long-time regime for small but nonzero level spacing.
Keywords
Cite
@article{arxiv.2206.00704,
title = {Emergence of Fermi's Golden Rule},
author = {Tobias Micklitz and Alan Morningstar and Alexander Altland and David A. Huse},
journal= {arXiv preprint arXiv:2206.00704},
year = {2022}
}
Comments
4 pages, 2 figures, supplementary material