Abstract
A quantum phase model is considered and the temporal evolution of the exponential of the first moment of particles distribution is studied. The calculation of the temporal evolution is based on the properties of Schur functions. The form-factor of the considered distribution function is expressed in the determinant form and it is proved that in the q-parametrization it is equal to the generating function of the norm-trace generating function of the boxed plane partitions. The asymptotics of the temporal evolution in the double scaling limit and decreasing temperature is obtained. It is shown that the amplitudes of the leading asymptotics depend on the generating function of plane partitions with the fixed sum of diagonal elements.
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