3,004 research outputs found

    Entanglement, quantum randomness, and complexity beyond scrambling

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    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

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    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.

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    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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