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We present a convenient way to evaluate the information entropy of a quantum mechanical state via the Glauber Q-representation. As an example we discuss the information entropy of a thermally relaxing squeezed state in terms of its Q-representation and show the validity of the corresponding entropic uncertainty- and Araki-Lieb inequalities.
The general theory of atomic angular momentum states is used to derive the Wigner distribution function for atomic angular momentum number states, coherent states, and squeezed states. These Wigner functions W(theta,phi) are represented as a pseudo-probability distribution in spherical coordinates theta and phi on the surface of a sphere of radius the square root of j(j +1) where j is the total angular momentum.
Correlated squeezed states for a quantum oscillator are constructed based on the method of quantum integrals of motion. The quantum oscillator is acted upon by short duration pulses. Three delta-kickings of frequency are used to model the pulses' dependence upon the time aspects of the frequency of the oscillator. Additionally, the correlation coefficient and quantum variances of operations of coordinates and momenta are written in explicit form.
The behavior of an electromagnetic field in an ideal cavity with an oscillating boundary is considered in the resonance long-time limit. The rates of photon creation from the vacuum and thermal states are evaluated. The squeezing coefficients for the field modes are found, as well as the backward reaction of the field on the vibrating wall.
Acetate concentrations and rates of acetate oxidation and sulfate reduction were measured in S. alterniflora sediments in New Hampshire and Massachusetts. Pore water extracted from cores by squeezing or centrifugation contained in greater than 0.1 mM acetate and, in some instances, greater than 1.0 mM. Pore water sampled nondestructively contained much less acetate, often less than 0.01 mM. Acetate was associated with roots, and concentrations varied with changes in plant physiology. Acetate turnover was very low whether whole core or slurry incubations were used. Radiotracers injected directly into soils yielded rates of sulfate reduction and acetate oxidation not significantly different from core incubation techniques. Regardless of incubation method, acetate oxidation did not account for a substantial percentage of sulfate reduction. These results differ markedly from data for unvegetated coastal sediments where acetate levels are low, oxidation rate constants are high, and acetate oxication rates greatly exceed rates of sulfate reduction. The discrepancy between rates of acetate oxidation and sulfate reduction in these marsh soils may be due either to the utilization of substrates other than acetate by sulfate reducers or artifacts associated with measurements of organic utilization by rhizosphere bacteria. Care must be taken when interpreting data from salt marsh sediments since the release of material from roots during coring may affect the concentrations of certain compounds as well as influencing results obtained when sediment incubations are employed.
The design requirements and initial design concept for the AXAF-I Science Instrument Module (SIM) were reviewed at Ball on September 29, 1993. The concept design SIM focus mechanism utilizes a planetary gearset, with redundant motors, to drive a large ring (called 'main housing bearing') via a spur gearset. This large drive ring actuates three tangent bar links (called 'push rods'), which in turn actuate three levers (called 'pin levers'). Each of the three pin levers rotates an 'eccentric pin,' which in turn moves the base of a bipod flexure in both the radial (normal to optical axis) and axial (focus along optical axis) directions. Three bipod flexures are employed, equally spaced at 120 degrees apart, the base of each being translated in the two directions as described above. A focus adjustment is made by rotating the drive ring, which drives the push rods and therefore the pin levers, which in turn rotate the eccentric pins, finally imparting the two motions to the base of each of the bipod flexures. The axial translation (focus adjustment) of the focused structure is the sum of the direct axial motion plus axial motion which comes from uniformly squeezing the three bipod bases radially inward. SAO documented the following concerns regarding the focus mechanism in memo WAP-FY94-001, dated October 7, 1993: (1) The focus adjustment depends, in large part, on the structural properties (stiffnesses and end fixities) of the bipod flexures, push rods, pin levers and eccentric pins. If these properties are not matched very well, then lateral translations as well as unwanted rotations of the focussed structure will accompany focus motion. In addition, the stackup of linkage tolerances and any nonuniform wear in the linkages will result in the same unwanted motions. Thermal gradients will also affect these motions. At the review Ball did not present supporting analyses to support their choice of this design concept. (2) The proposed 'primary' method of measuring focus is by counting motor steps. The 'backup' method is by a pot mounted on the drive ring. Neither method provides for a direct measurement of the quantity desired (focus position). This is of concern because of the long and indirect relationship between focus and the sensed quantity (drive ring rotation). There are three sinusoidal relationships and structural stiffness in the path, and the resulting calibration is likely to be highly nonlinear. These methods would require an accurate ground calibration. (3) Ground calibration (and verification) of focus vs. drive position must be done in 1-g on the ground. This calibration will be complicated by both the structural characteristics of the bipods and the fact that the CG of the translating portion of the SIM is not on the optical axis (thereby causing unwated rotations and changing the focus position vs. motor step and pot readout relationships). The SIM translating weight could be offloaded, but the calibration then becomes sensitive to any errors in offloading (both magnitude and direction). There are concerns as to whether a calibration to the required accuracy can be accomplished on the ground. (4) The choice of a potentiometer as the focus position sensor is questionable in terms of reliability for a five year mission. The results of SAO's study of items 1, 2 and 3 described above are presented in this report.
The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.
Electromagnetic fields of the vacuum mode near a conducting mirror are modified with respect to those in free space, with their amplitudes having a sinusoidal spatial dependence from the mirror. Therefore if we combine this spatially amplitude-modulated vacuum field mode and intense coherent light with a beam splitter, we may detect this fluctuation of the vacuum mode in a homodyne detection scheme. It will give a new method to produce squeezed states of light with a single mirror placed close to an unused port of a beam splitter. We show that the amplitude fluctuation of the combined light can be reduced by a factor of 2 below that of the coherent light. We also discuss the limitations due to the finite line width of the laser and the effective absorption length of the photodiodes.
The possibility of using the phase space formalism to establish a correspondence between the dynamical behavior of squeezed states and optical or charged beams, propagating through linear systems, has received a great deal of attention during the last years. In this connection, it has been indicated how optical experiments may be conceived to measure the Wigner rotation angle. In this paper we address the topic within the context of the paraxial propagation of optical or charged beams and suggest a possible experiment for measuring the Wigner angle using an electron beam passing through quadrupoles and drift sections. The analogous optical system is also discussed.
The model describing three coupled quantum oscillators with decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. Due to the Manley-Rowe relations the problem of exact eigenvalues and eigenstates is reduced to the calculation of new orthogonal polynomials defined both by the difference and differential equations. The quantum statistical properties are examined in the case when initially: the Stokes mode is in the vacuum state; the Rayleigh mode is in the number state; and the vibration mode is in the number of or squeezed states. The collapses and revivals are obtained for different initial conditions as well as the change in time the sub-Poisson distribution by the super-Poisson distribution and vice versa.
At this writing, Clementine had successfully fulfilled its moon-mapping mission; at this reading it will have also, with continued good fortune, taken a close look at the asteroid Geographos. The thermal design that made all this possible was indeed formidable in many respects, with very high ratios of requirements-to-available resources and performance-to-cost and mass. There was no question that a test verification of this quite unique and complex design was essential, but it had to be squeezed into an unyielding schedule and executed with bare-bones cost and manpower. After describing the thermal control subsystem's features, we report all the drama, close-calls, and cost-cutting, how objectives were achieved under severe handicap but (thankfully) with little management and documentation interference. Topics include the newly refurbished chamber (ready just in time), the reality level of the engineering model, using the analytical thermal model, the manner of environment simulation, the hand-scratched film heaters, functioning of all three types of heat pipes (but not all heat pipes), and the BMDO sensors' checkout through the chamber window. Test results revealed some surprises and much valuable data, resulting in thermal model and flight hardware refinements. We conclude with the level of correlation between predictions and both test temperatures and flight telemetry.
The geometrical parameters for a wormgear intended to be used as the transmission in advanced helicopters are finalized. The resulting contact pattern of the meshing tooth surfaces is suitable for the implementation of hydrostatic lubrication Fluid film lubrication of the contact is formulated considering external pressurization as well as hydrodynamic wedge and squeeze actions. The lubrication analysis is aimed at obtaining the oil supply pressure needed to separate the worm and gear surfaces by a prescribed minimum film thickness. The procedure of solving the mathematical problem is outlined.
Alternative algebraic techniques to approximate a given Hamiltonian by a harmonic oscillator are described both for time-independent and time-dependent systems. We apply them to the description of a one dimensional atom-diatom collision. From the resulting evolution operator, we evaluate vibrational transition probabilities as well as other time-dependent properties. As expected, the ground vibrational state becomes a squeezed state during the collision.
The scalar quantum field uniformly moving plates in three dimensional space is studied. Field equations for Dirichlet boundary conditions are solved exactly. Comparison of the resulting wavefunctions with their instantaneous static counterpart is performed via Bogolubov coefficients. Unlike the one dimensional problem, 'particle' creation as well as squeezing may occur. The time dependent Casimir energy is also evaluated.
It is shown that the even and odd coherent light and other nonclassical states of light like superposition of coherent states with different phases may replace the squeezed light in an interferometric gravitational wave detector to increase its sensitivity.
In this talk we re-examine three important properties of quantum laser systems: (1) photon counting statistics; (2) squeezing; and (3) signal-to-quantum noise ratio. None of these phenomena depends on the choice of hamiltonian; indeed, we analyze them initially without restriction to any specific form of the commutation relations.
Waviness and tow misalignment are often cited as possible causes of data scatter and lower compression stiffness and strength in textile composites. Strength differences of as much as 40 percent have been seen in composites that appear to have the same basic material and structural properties -- i.e., yarn orientation, yarn size, interlacing geometry. Fabric geometry distortion has been suggested as a possible reason for this discrepancy, but little quantitative data or substantial evidence exists. The focus of this research is to contribute to the present understanding of the causes and effects of geometric distortion in textile composites. The initial part of the study was an attempt to gather qualitative information on a variety of textile structures. Existing and new samples confirmed that structures with a significant direction presence would be more susceptible to distortion due to the compaction process. Thus, uniweaves (fiber vol frac: 54-72 percent) biaxial braids (vf: 34-58 percent) demonstrated very little fabric geometry distortion. In stitched panels, only slight buckling of z-direction stitches was observed, primarily near the surface. In contrast, for structures with high compaction ratios -- e.g., large cylindrical yarns (2.5:1) orpowder towpreg (4:1) -- there were visible distortions where previously smooth and periodic undulations were transformed to abrupt changes in direction. A controlled study of the effect of forming pressure on distortion was conducted on type 162 glass plain weave fabrics. Panels (6 x 6 in) were produced via a resin infusion type setup, but with an EPON 815 epoxy resin. Pressures ranging from hand layup to 200 psi were used (vf: 34-54 percent). Photomicrographs indicated that at pressures up to 50 psi, large changes in thickness were due primarily to resin squeeze out. At higher pressures, when intimate contact was made between the layers, there was some tow flattening and in-plane shifting to optimize nesting. However, even at 200 psi the period and amplitude of the tow undulation remained constant, suggesting that for this relatively fine fabric, distortions from compaction were not a problem. Because of the interest in using larger tows (to reduce cost) and more complex structures, tests were also run on 2D triaxial glass braid (113 yd/lb at 0, 225 yd/lb at +/- 45). Forming pressures of 20, 50, 200, and 500 psi were used, and short block compression tests were run. The 500 psi specimen had a 10 percent decrease in modulus and an almost 50 percent decrease in strength (vs. 20 psi). Because the total fiber wgt/panel was kept constant, the thickness varied from 0.32 to 0.22 in (49-70 percent vf). Yet, the strength value is clearly below what would be expected, even with the decrease in thickness. Photomicrographs of these samples will be taken to determine if more fabric distortion exists in the 500 psi specimens. Finally, because the ultimate goal is to be able to predict and control distortion in a variety of textile structures, a model compaction test was developed to directly measure the deformation of the tows during compaction. Layers of dry glass fabric were placed in a mold with a clear plexiglass window. The yarn amplitude and period was then calculated using image analysis of the videotaped deformation. Preliminary tests demonstrated the feasibility of this technique for simple fabrics with large tows.
The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.