3,004 research outputs found
Entanglement, quantum randomness, and complexity beyond scrambling
Scrambling is a process by which the state of a quantum system is effectively
randomized due to the global entanglement that "hides" initially localized
quantum information. In this work, we lay the mathematical foundations of
studying randomness complexities beyond scrambling by entanglement properties.
We do so by analyzing the generalized (in particular R\'enyi) entanglement
entropies of designs, i.e. ensembles of unitary channels or pure states that
mimic the uniformly random distribution (given by the Haar measure) up to
certain moments. A main collective conclusion is that the R\'enyi entanglement
entropies averaged over designs of the same order are almost maximal. This
links the orders of entropy and design, and therefore suggests R\'enyi
entanglement entropies as diagnostics of the randomness complexity of
corresponding designs. Such complexities form a hierarchy between information
scrambling and Haar randomness. As a strong separation result, we prove the
existence of (state) 2-designs such that the R\'enyi entanglement entropies of
higher orders can be bounded away from the maximum. However, we also show that
the min entanglement entropy is maximized by designs of order only logarithmic
in the dimension of the system. In other words, logarithmic-designs already
achieve the complexity of Haar in terms of entanglement, which we also call
max-scrambling. This result leads to a generalization of the fast scrambling
conjecture, that max-scrambling can be achieved by physical dynamics in time
roughly linear in the number of degrees of freedom.Comment: 72 pages, 4 figures. Rewritten version with new title. v3: published
versio
Analyses of celestial pole offsets with VLBI, LLR, and optical observations
This work aims to explore the possibilities of determining the long-period
part of the precession-nutation of the Earth with techniques other than very
long baseline interferometry (VLBI). Lunar laser ranging (LLR) is chosen for
its relatively high accuracy and long period. Results of previous studies could
be updated using the latest data with generally higher quality, which would
also add ten years to the total time span. Historical optical data are also
analyzed for their rather long time-coverage to determine whether it is
possible to improve the current Earth precession-nutation model
The electromagnetic performance of brushless permanent magnet DC motors - with particular reference to noise and vibration.
A comprehensive analytical technique is developed for predicting the instantaneous
magnetic field distribution in radial-field, surface-mounted permanent magnet brushless DC
motors under any load condition and commutation strategy. It is based on a 2-dimensional
analysis in polar coordinates and accounts implicitly for the corresponding stator winding current
waveforms and the effect of stator slot openings. In addition, a 2-dimensional analytical method
for calculating the back-emf waveform is presented, whilst the analytical technique is applied to
the prediction of the cogging torque waveform and the calculation of the self- and
mutual-winding inductances.
Also developed and validated is an analytical model for predicting the steady-state dynamic
performance of a 3-phase brushless DC drive, by exploiting the periodicity in the stator winding
voltage and current waveforms, with due account of the influence of commutation events in the
inverter bridge, the back-emf waveform, current limiting, and commutation timing etc. The
model is developed further to couple with the motion equation of the rotor to enable the transient
and steady-state dynamic performance of brushless DC drives to be predicted.
The effect of end-shields on the vibrational behaviour of stators is investigated by the modem
modal analysis technique, and new formulae for the calculation of the acoustic power radiated
by a cylindrical stator of finite length, using an analytical method, are presented. A technique
which combines the finite element method and Fourier analysis to account for the effects of
end-shields on the acoustic radiation is developed, and the spherical acoustic radiation model of
motors has been improved by the application of finite elements. Finally, a systematic analytical
approach to the estimation and analysis of the acoustic noise from a radial-field, internal rotor,
brushless DC motor is presented
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