Emergence of Fermi's Golden Rule
- URL: http://arxiv.org/abs/2206.00704v1
- Date: Wed, 1 Jun 2022 18:35:21 GMT
- Title: Emergence of Fermi's Golden Rule
- Authors: Tobias Micklitz, Alan Morningstar, Alexander Altland, and David A.
Huse
- Abstract summary: Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a 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.
- Score: 55.73970798291771
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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