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

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.Comment: 16 pages, Contribution for the proceedings of QMath13: Mathematical Results in Quantum Physics, Atlanta, 201

On the Regime of Localized Excitations for Disordered Oscillator Systems

We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with arbitrarily large energy density. We prove zero-velocity Lieb-Robinson bounds for the dynamics of Weyl operators as well as for position and momentum operators restricted to this regime. Dynamical localization is also shown in the form of quasi-locality of the time evolution of local Weyl operators and through exponential clustering of the dynamic correlations of states with localized excitations

Tell Me Why You Smile, Mona Lisa?

Portrait of Mona Lisa with sky in backgroundhttps://scholarsjunction.msstate.edu/cht-sheet-music/11525/thumbnail.jp

Entanglement Dynamics of Disordered Quantum XY Chains

We consider the dynamics of the quantum XY chain with disorder under the general assumption that the expectation of the eigenfunction correlator of the associated one-particle Hamiltonian satisfies a decay estimate typical of Anderson localization. We show that, starting from a broad class of product initial states, entanglement remains bounded for all times. For the XX chain, we also derive bounds on the particle transport which, in particular, show that the density profile of initial states that consist of fully occupied and empty intervals, only have significant dynamics near the edges of those intervals, uniformly for all times.Comment: 22 pages, final version, to appear in Lett. Math. Phy

Sal - O - May (Salome) : Song Of The Orient And Fox Trot

https://digitalcommons.library.umaine.edu/mmb-vp/3357/thumbnail.jp