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

AU - Stolz, Günter

N1 - Publisher Copyright:
© 2018 by the authors.

PY - 2018

Y1 - 2018

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.

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U2 - 10.1090/conm/717/14439

DO - 10.1090/conm/717/14439

M3 - Chapter

AN - SCOPUS:85059766133

T3 - Contemporary Mathematics

SP - 31

EP - 47

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -