Response of a canonical ensemble of quantum oscillators to a random metric

We calculate the susceptibility of a canonical ensemble of quantum oscillators to the singular random metric. If the covariance of the metric is $\vert {\bf x}-{\bf x}^{\prime}\vert^{-4α}$ $0< α<\frac{1}{2}$ then the expansion of the partition function in powers of the temperature involves non-integer indices.

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