Disorder in the spectral function of a qubit ensemble

The impact of disorder in the vibrational bath of an ensemble of open quantum systems is explored, arising either from variation in the overall coupling strength or from uncertainty in the shape of the environment spectral function. Such disorder leads to an additional source of decoherence of subsystem ensembles, due to variation in the reorganization energy. Additionally, vibrational disorder induces a shift in the oscillation frequency of the coherence between ground and excited states. This shift is temperature dependent, and in the high temperature limit $\delta \omega \propto T$. This latter finding could be of particular relevance to biological systems exhibiting long lived coherences in highly disordered environments, where temperature-dependent quantum beats have been observed.