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## The Decay of a Fock State

The Fock state is the most mathematically simple field state. A 1989 paper by Ning Lu at the University of New Mexico examines the decay of a Fock state interacting with a thermal reservoir at absolute zero.[21] Set the number of field states to one hundred and make the field a Fock state with n=99 (Remember that there is a n=0 state) and set . The plot that Ning Lu obtained from his analytical work is reproduced in Figure .

Figure: Analytical Solution to the Damping of a Fock State at n=99 and

Run FieldApp and examine the field at t=1, t=0.1, and t=0.01 seconds. FieldApp predicts the same values as the analytical calculation by Lu. This article focused on an effect which surprised Lu. He equated the lifetime of the field with the lifetime of the field states. FieldApp clearly demonstrates that this equality is invalid.

The lifetime of the field is the amount of time necessary for the field to decay to a thermal state, which at absolute zero is the vacuum state. The lifetime of a field state is the amount of time that a single exists. n=99 has zero probability well before the field has reached the vacuum state. This problem is trivial to solve with FieldApp because this program provides a way of visualizing the decaying field in real time. The analytical solution of this problem does not provide this aid.

Since FieldApp solves this problem numerically, it can analyze the decay of a Fock state with an arbitrary temperature. Set to some non--zero value and run FieldApp. How is this result different from the plot above? Are the decay times the same?

Andy Antonelli
Wed May 17 14:34:24 EDT 1995