### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

**Correlations in disordered quantum harmonic oscillator systems : The effects of excitations and quantum quenches.** / Abdul-Rahman, Houssam; Sims, Robert J; Stolz, Günter.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Correlations in disordered quantum harmonic oscillator systems

T2 - The effects of excitations and quantum quenches

AU - Abdul-Rahman, Houssam

AU - Sims, Robert J

AU - Stolz, Günter

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85059766133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059766133&partnerID=8YFLogxK

U2 - 10.1090/conm/717/14439

DO - 10.1090/conm/717/14439

M3 - Chapter

VL - 717

SP - 31

EP - 47

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -