We have used matrix continued fraction methods pioneered previously, to solve essentially exactly for the dynamics of the one 85Rb atom micromaser. A range of cavity Q values and of average atomic input rates R equals Tp-1 and of atomic interaction times tint is studied. For Tp approximately greater than 200tint the system does evolve to a steady state. And even Q equals 5 multiplied by 1010 and temperature T equals 0.070 degrees K are apparently insufficient to avoid evolution to a steady state with finite variance of the cavity field when tint equals 1.54/44 kHz unless Tp is also substantially reduced. Only in this way are actual trapping state dynamics obtained. The field variance v is not a good diagnostic for observing such trapping state dynamics.
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