Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches

Houssam Abdul-Rahman, Robert J Sims, Günter Stolz

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages31-47
Number of pages17
Volume717
DOIs
StatePublished - Jan 1 2018

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Harmonic Oscillator
Decay Estimates
Excitation
Disorder
Momentum
Decay
Model

ASJC Scopus subject areas

  • Mathematics(all)

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

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

Contemporary Mathematics. Vol. 717 American Mathematical Society, 2018. p. 31-47.

Research output: Chapter in Book/Report/Conference proceedingChapter

Abdul-Rahman, H, Sims, RJ & Stolz, G 2018, Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches. in Contemporary Mathematics. vol. 717, American Mathematical Society, pp. 31-47. https://doi.org/10.1090/conm/717/14439
Abdul-Rahman H, Sims RJ, Stolz G. Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches. In Contemporary Mathematics. Vol. 717. American Mathematical Society. 2018. p. 31-47 https://doi.org/10.1090/conm/717/14439
Abdul-Rahman, Houssam ; Sims, Robert J ; Stolz, Günter. / Correlations in disordered quantum harmonic oscillator systems : The effects of excitations and quantum quenches. Contemporary Mathematics. Vol. 717 American Mathematical Society, 2018. pp. 31-47
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