### Abstract

We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends on the magnitude of the maximally excited mode. Then, we consider the situation of a quantum quench. We prove that the full time-evolution of an initially chosen (uncorrelated) product state has disorder-averaged correlations which decay exponentially in space, uniformly in time.

Original language | English (US) |
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Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 31-47 |

Number of pages | 17 |

Volume | 717 |

DOIs | |

State | Published - Jan 1 2018 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Abdul-Rahman, H., Sims, R. J., & Stolz, G. (2018). Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches. In

*Contemporary Mathematics*(Vol. 717, pp. 31-47). American Mathematical Society. https://doi.org/10.1090/conm/717/14439