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 -