Set up the field in a thermal state with . Examine the probability of finding the atom in the upper state. Run the program for several hundred seconds and examine Figure .
Figure: A thermal state has a chaotic character.
This plots periodicity is infinite, i.e., it is chaotic. Thermal radiation is often called chaotic light because it has no order. The effect of thermal radiation is most unlike a Fock state. A Fock state is a single sinusoidal oscillation of frequency where n is the Fock state's number. Thermal radiation is a distribution of such oscillations. The distribution defines which of the infinite possible field eigenfunctions will couple to the atom and thus what effect the field mode will have on the atom. All the information about this interaction is housed within the photon statistics.
This chaotic effect was always present in the thermal state's photon statistics but did not manifest itself until the field was coupled to the atom. Remember that many of the averages and variances of the field were the same for both the Fock and Thermal states; yet, they were different. The way to uncover their inherent difference was to allow them to interact with an atom.
In FieldApp we showed that all fields decay into thermal states. All states, no matter their initial order, will ultimately become chaotic if the field is interacting with a thermal reservoir. Thus, somewhere in the evolution between these two field states a transition to chaos occurs.