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Completing Fermi's golden rule: the origin of transition rates in open systems

August 5, 2015 - 2:00pm
Kurt Jacobs
Army Research Laboratory
Fermi's golden rule is widely used, and the resulting transition rates are an important 
part of the thermal behaviour of open quantum systems. But this rule is curious because it is valid 
outside the regime in which it is derived: It is derived only for short times and for off-resonant 
transitions but works for all times and for resonant transitions. Here we show analytically 
that an interaction with a resonant, dense spectrum induces a rate equation for all times, giving 
essentially exact exponential decay in the appropriate regime. From this analysis we are able to 
extract the decay rate, which is indeed the rate of Fermi's golden rule (with a small correction), the 
short, non-Markovian time period before which the rate equation sets in, and determine the parameter 
regime required for this behavior. Our analysis provides the start of a more solid foundation on 
which to model thermal baths in terms of interactions with dense spectra.  
3100A Computer and Space Sciences
College Park, MD 20742