Yes by the equipartition theorem there’s an average of kT of energy in each standing wave mode at any given moment. Might be fun to calculate how many left-right atoms that corresponds to—I think that calculation should be doable. I imagine that for the fundamental mode, it would be comparable to the √(number of atoms in the box) difference that we expect for other reasons.
It’s continuous and exponential. If amplitude of standing wave mode N decays by a factor of 2 in X seconds, then it‚ it’s the same X whether the initial amplitude in that mode is macroscopic versus comparable-to-the-noise-floor. (Well, unless there are nonlinearities / anharmonicities, but that’s probably irrelevant in this context.) But meanwhile, noise is driving the oscillation too. So anyway, I think it really matters how X compares to 20 seconds, which again is something I don’t know.
Yes by the equipartition theorem there’s an average of kT of energy in each standing wave mode at any given moment. Might be fun to calculate how many left-right atoms that corresponds to—I think that calculation should be doable. I imagine that for the fundamental mode, it would be comparable to the √(number of atoms in the box) difference that we expect for other reasons.
It’s continuous and exponential. If amplitude of standing wave mode N decays by a factor of 2 in X seconds, then it‚ it’s the same X whether the initial amplitude in that mode is macroscopic versus comparable-to-the-noise-floor. (Well, unless there are nonlinearities / anharmonicities, but that’s probably irrelevant in this context.) But meanwhile, noise is driving the oscillation too. So anyway, I think it really matters how X compares to 20 seconds, which again is something I don’t know.