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

TL;DR

This paper investigates how a collection of quantum oscillators responds to a singular random metric, revealing non-integer power expansions in the partition function influenced by the metric's covariance.

Contribution

It introduces a novel analysis of quantum oscillators' susceptibility to singular random metrics, highlighting the impact of metric covariance on thermodynamic expansions.

Findings

Partition function expansion involves non-integer indices for certain covariance parameters.

Susceptibility depends on the singular behavior of the random metric.

The study provides insights into quantum systems in irregular geometric backgrounds.

Abstract

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