Response of a Canonical Ensemble of Quantum Oscillators to a Random Metric

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