1,173 research outputs found
Correlations Estimates in the Lattice Anderson Model
We give a new proof of correlation estimates for arbitrary moments of the
resolvent of random Schr\"odinger operators on the lattice that generalizes and
extends the correlation estimate of Minami for the second moment. We apply this
moment bound to obtain a new -level Wegner-type estimate that measures
eigenvalue correlations through an upper bound on the probability that a local
Hamiltonian has at least eigenvalues in a given energy interval. Another
consequence of the correlation estimates is that the results on the Poisson
statistics of energy level spacing and the simplicity of the eigenvalues in the
strong localization regime hold for a wide class of translation-invariant,
selfadjoint, lattice operators with decaying off-diagonal terms and random
potentials.Comment: 16 page
Comparison of Simulator Wear Measured by Gravimetric vs Optical Surface Methods for Two Million Cycles
Understanding wear mechanisms are key for better implants
Critical to the success of the simulation
Small amount of metal wear can have catastrophic effects in the patient such as heavy metal poisoning or deterioration of the bone/implant interface leading to implant failure
Difficult to measure in heavy hard-on-hard implants (metal-on-metal or ceramic-on-ceramic)
May have only fractions of a milligram of wear on a 200 g component
At the limit of detection of even high-end balances when the component is 200 g and the change in weight is on the order of 0.000 1 grams
Here we compare the standard gravimetric wear estimate with
A non-contact 3D optical profiling method at each weighing stop
A coordinate measuring machine (CMM) at the beginning and end of the ru
Quantum harmonic oscillator systems with disorder
We study many-body properties of quantum harmonic oscillator lattices with
disorder. A sufficient condition for dynamical localization, expressed as a
zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the
eigenfunction correlators for an effective one-particle Hamiltonian. We show
how state-of-the-art techniques for proving Anderson localization can be used
to prove that these properties hold in a number of standard models. We also
derive bounds on the static and dynamic correlation functions at both zero and
positive temperature in terms of one-particle eigenfunction correlators. In
particular, we show that static correlations decay exponentially fast if the
corresponding effective one-particle Hamiltonian exhibits localization at low
energies, regardless of whether there is a gap in the spectrum above the ground
state or not. Our results apply to finite as well as to infinite oscillator
systems. The eigenfunction correlators that appear are more general than those
previously studied in the literature. In particular, we must allow for
functions of the Hamiltonian that have a singularity at the bottom of the
spectrum. We prove exponential bounds for such correlators for some of the
standard models
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