Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator

Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the Wigner function. On all levels of approximation, these evolution equations retain the periodicity of the driving, so that their solutions have Floquet form and represent eigenfunctions of a non-unitary propagator over a single period of the driving. We discuss asymptotic states in the long-time limit as well as the conservative and the high-temperature limits. Numerical results obtained within the different Markov approximations are compared with the exact path-integral solution. The application of the improved Floquet-Markov scheme becomes increasingly important when considering stronger driving and lower temperatures.Comment: 29 pages, 7 figure

Lubrication And Seal Oil Systems - Common Problems And Practical Solutions.

LecturePg. 51-64Current technologies now make it possible to build turbomachinery without the need for a lubrication and seal oil system. However, there is an established machinery population that still requires support systems for oil wetted bearings and seals. For most companies, it is not economically practical to convert to new bearings and seals to eliminate the oil support system. Indeed, this may not be the best solution in many cases. Lubrication and seal oil systems can be the single largest cause of spurious and nuisance trips. In most cases, such trips are due to controller degradation, improper operation, or simple neglect. The most common causes of oil system problems, and practical solutions aimed at long term operating reliability are addressed. A chronic cause of spurious trips is oil pump switchover. Usually, such problems can be eliminated by upgrading controllers and/or control valve selection philosophy, installation of hydraulic pulsation dampeners, a design audit of the piping configuration, and, very often, operating procedures. Oil system instability contributes significantly to nuisance trips. Again, a review of system control components and associated hardware can usually minimize this phenomenon. Additionally, improper purging of air has been known to cause similar problems, and frustrate the most experienced operator. There are other problems which can also result in unscheduled downtime of critical rotating machinery. These include collapsing oil filter elements, improper sour seal oil drainer sizing, improper control valve sizing, lack of attention to transient conditions, controller and pressure switch physical location, and oil cooler integrity, to name a few. There is a large installed machinery population that has been in operation for many years, but has never been upgraded to present standards. New developments in control technology lend themselves to increasing oil system reliability, in addition to other component upgrades. Refineries and chemical plants now commonly utilize comprehensive preventive maintenance (PM) programs; however, oil systems do not seem to be included in such programs to the same level as that of their supported machinery. Oil system reliability can be increased, and nuisance trips minimized, by monitoring several key operating points which include valve position, oil temperature and chemical analysis, and filter differential pressure (to name a few) on a scheduled basis. Such data can also be useful in determining or predicting problems with the rotating equipment. It has also become obvious in recent years that process demands, in addition to efforts to improve oil system reliability, have resulted in systems that are more complex. Such complexity has, in some cases, ironically decreased operational reliability due to the introduction of unnecessary hardware. Practical and realistic basic design guidelines will be presented, along with a comparison of the various design philosophies currently being utilized in the industry

Decoherence and Initial Correlations in Quantum Brownian Motion

We analyze the evolution of a quantum Brownian particle starting from an initial state that contains correlations between this system and its environment. Using a path integral approach, we obtain a master equation for the reduced density matrix of the system finding relatively simple expressions for its time dependent coefficients. We examine the evolution of delocalized initial states (Schr\"odinger's cats) investigating the effectiveness of the decoherence process. Analytic results are obtained for an ohmic environment (Drude's model) at zero temperature.Comment: 15 pages, RevTex, 5 figures included. Submitted to Phys. Rev.

Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

We consider the Brownian motion of a quantum mechanical particle in a one-dimensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dependent position and momentum variances are compared with results of an iterative algorithm, the so-called quasiadiabatic propagator path integral algorithm (QUAPI). We obtain good agreement over an extended range of parameters for this spatially continuous quantum system. These findings indicate the reliability of the algorithm also in cases for which analytic results may not be available a priori.Comment: 15 pages including 11 figures, one reference added, minor typos correcte