> From quantum field theory, you get polynomial decay
I think you're oversimplifying, although I agree that I was also oversimplifying when I said that the theory predicts exact exponential decay.
What I get from that stack exchange thread and the linked papers is this: in an idealized (and not physically possible for a real system) model in which every individual decay is statistically independent from every other and in which all of the quantum states that are possible end points of the decay are unoccupied, the theory predicts exact exponential decay. But in real physical systems, neither of those conditions is exactly true. Individual members of an ensemble of decaying quantum systems (such as radioactive atoms in a sample) interact with each other (either directly or indirectly via states in the environment), so their decays are not completely independent; and any real decaying system has an external environment which includes some occupied "target" quantum states. When these effects are taken into account, the theory predicts a decay law which is often called "power law" but which I would describe as more of a "truncated exponential": it replaces an infinite series of power law terms (the exact exponential) with a finite number of them. The actual measured decay law in a given experiment will depend on how much the experiment probes the portion of the state space where the above effects are significant (for example, a decay law measured over a very long time can deviate measurably from exponential where a measurement over a shorter time would not).
AFAIR if you have a single excited particle, you still get this polynomial decay. (It was more about every distribution and Fourier transform properties - as mentioned in the post.)
Yes, in these subtle effects backaction may be important. (The whole non-exponential decay is because the "emitted" EM field acts back on the particle.)
> AFAIR if you have a single excited particle, you still get this polynomial decay.
I'm not seeing that in the linked papers. I'm seeing descriptions of exponential decay under certain conditions, and deviations from that under other conditions.
I think you're oversimplifying, although I agree that I was also oversimplifying when I said that the theory predicts exact exponential decay.
What I get from that stack exchange thread and the linked papers is this: in an idealized (and not physically possible for a real system) model in which every individual decay is statistically independent from every other and in which all of the quantum states that are possible end points of the decay are unoccupied, the theory predicts exact exponential decay. But in real physical systems, neither of those conditions is exactly true. Individual members of an ensemble of decaying quantum systems (such as radioactive atoms in a sample) interact with each other (either directly or indirectly via states in the environment), so their decays are not completely independent; and any real decaying system has an external environment which includes some occupied "target" quantum states. When these effects are taken into account, the theory predicts a decay law which is often called "power law" but which I would describe as more of a "truncated exponential": it replaces an infinite series of power law terms (the exact exponential) with a finite number of them. The actual measured decay law in a given experiment will depend on how much the experiment probes the portion of the state space where the above effects are significant (for example, a decay law measured over a very long time can deviate measurably from exponential where a measurement over a shorter time would not).