Emergence of Fermi's Golden Rule
arXiv:2206.00704 · doi:10.1103/PhysRevLett.129.140402
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.
4 pages, 2 figures, supplementary material
References in corpus (6)
- Introduction to Random Matrices - Theory and Practice
- How a small quantum bath can thermalize long localized chains
- Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
- Onset of many-body quantum chaos due to breaking integrability
- Are many-body localized systems stable in the presence of a small bath?
- Quantum ergodicity in the many-body localization problem