Quantum Entanglement at High Temperatures? II. Bosonic Systems in Nonequilibrium Steady State

This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures $T_1 > T_2$. For \textit{constant bilinear inter-oscillator coupling} studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature $T_c$. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on $T_{1}$, $T_{2}$ , the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature $T_c$ is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, `hot entanglement' is largely a fiction. In Paper III we will examine the case (C2) of \textit{time-dependent driven coupling } which contains the parametric pumping type described in [2] wherein entanglement was first shown to sustain at high temperatures.Comment: 47 pages, 9 figure

A tool for metadata analysis

We describe a Web-based metadata quality tool that provides statistical descriptions and visualisations of Dublin Core metadata harvested via the OAI protocol. The lightweight nature of development allows it to be used to gather contextualized requirements and some initial user feedback is discussed

Effect of extended tooth contact on the modeling of spur gear transmissions

In some gear dynamic models, the effect of tooth flexibility is ignored when the model determines which pairs of teeth are in contact. Deflection of loaded teeth is not introduced until the equations of motion are solved. This means the zone of tooth contact and average tooth meshing stiffness are underestimated and the individual tooth load is overstated, especially for heavily-loaded gears. The static transmission error and dynamic load of heavily-loaded, low-contact-ratio spur gears is compared with this effect both neglected and included. Neglecting the effect yields an underestimate of resonance speeds and an overestimate of the dynamic load

Influence of linear profile modification and loading conditions on the dynamic tooth load and stress of high contact ratio gears

A computer simulation for the dynamic response of high-contact-ratio spur gear transmissions is presented. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. It is shown that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads

Effect of operating conditions on gearbox noise

Low contact ratio spur gears were tested in the NASA gear noise rig to study the noise radiated from the top of the gearbox. The measured sound power from the gearbox top was obtained from a near field acoustic intensity scan taken at 63 nodes just above the surface. The sound power was measured at a matrix of 45 operating speeds and torque levels. Results are presented in the form of a spectral speed map and as a plot of sound power versus torque (at constant speed) and as sound power versus speed (at constant torque). Because of the presence of vibration modes, operating speed was found to have more impact on noise generation than torque level. A NASA gear dynamics code was used to compute the gear tooth dynamic overload at the same 45 operating conditions used for the experiment. Similar trends were found between the analytical results for dynamic tooth overload and experimental results for sound power. Dynamic analysis may be used to design high quality gears with profile relief optimized for minimum dynamic load and noise