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Second quantization techniques for describing elastic and inelastic interactions between nonidentical composite bodies are presented and are applied to nucleus-nucleus collisions involving ground-state and one-particle-one-hole excitations. Evaluations of the resultant collision matrix elements are made through use of Wick's theorem.
Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.
Frequency locked loop /FLL/ to optimize loop filter and quantization of amplitude channel
A heuristic description is given for a simple harmonic oscillator as a basis for a model of anharmonicity. A formalism is applied in the process, which applies to complex excitation fields involving particle clusters and also facilitates a description of nonequilibrium multibody configurations by classical methods. The heuristic description is based on Streit's results (1965) and is free of linearization requirements in most physically interesting situations.
The development of optical fibers, lasers, and mixers at optical frequencies has offered the hope that active methods can contribute to optical interferometry. Heterodyning, in particular, looks attractive, even though bandwidths are narrower than one would like at present; one might expect this limitation to lessen as technology develops. That expectation, unfortunately, is not likely to benefit interferometry at optical wavelengths because of the intervention of quantum mechanics and the second law of thermodynamics, as Burke (1985a) pointed out. So much 'second quantization' noise is generated that only at infrared frequencies, somewhere in the 10-100 micron range, can one look forward to heterodyning in any realistic sense. The reason is easily understood. Every amplifier, in the quantum limit, works by stimulated emission, even though this basic truth is not obvious at radio frequencies. This means that there must be spontaneous emission occurring within every amplifier, and Strandberg (1957) showed that this implied a limiting noise temperature, T sub N = h nu/k, for any amplifier. Burke (1969) used this result to demonstrate that, if it were not for this quantum noise, the VLBI method would allow one to tell which slit a photon went through before forming an interference pattern, thus violating basic tenants of quantum mechanics. In essence, the second quantization condition Delta N Delta phi greater than or = 1 saves one from paradox. One can state the conclusion simply: any amplifier produces approximately one photon per Hertz of bandwidth. In optical interferometry, one will certainly want bandwidth in the 10(exp 12) to 10(exp 14) Hz range, and that implies an intolerable cacophony of noise photons. Only at infrared frequencies can one tolerate the quantum noise, where the natural noise background may be high and the mixers are not as efficient as one would hope for. The crossover at present is about 10 or 20 microns, but the boundary will shift to longer wavelengths as noise performance improves. One might guess that ultimately a wavelength of about 100 microns will mark the limit of useful amplification and heterodyning in astronomical aperture synthesis interferometry.
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Second quantization formalism for deriving Pariser-Parr-Pople model for planar unsaturated molecules, analyzing model by propagator or Green function methods
It has been proposed recently that the description of a many-body system with anharmonic coupling could be achieved through the use of the generalized Bose operators of Brandt and Greenberg (1969) directly in a second quantized form. The present study describes a new formulation of the generalized Bose operators which exploits the group theoretical content of these operators.
The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.
The spectral properties of ridge-waveguide graded-index separate-confinement heterostructure single-quantum-well (SQW) GaAs/AlGaAs lasers are measured. Long-cavity lasers (800 microns) exhibit remarkably pure CW single-longitudinal-mode spectra in spite of the short cavity mode spacing. At output power 5 mW, the sidemode suppression exceeds 24 dB and the linewidth is 1.5 MHz. The linewidth-power product (LPP) is 6.4 MHz mW. Measurements of LPP as a function of cavity length L gives a 1/L-squared dependence, in agreement with theory. The results are used to deduce the linewidth enhancement factor alpha at the gain peak wavelength and its dependence on the excitation level. The sublinear gain-carrier density relation in the SQW results in an increase in alpha with increasing carrier density (decreasing cavity length). A decrease in alpha was observed for lasers operating at the second quantized state due to a recovery of the differential gain.
The observation of photon-assisted resonant tunneling in a multiple quantum well structure composed of doped quantum wells separated by variably space superlattice energy filters is reported. Electrons confined in the quantum wells are excited to the second quantized state by intersubband absorption of incident infrared radiation and are subsequently emitted through the filters under appropriate bias conditions. This is manifested by a distinct peak, with an associated negative differential photoconductance, in the photocurrent versus bias voltage characteristic at low temperatures.
Specific configurations of first and second order all digital phase locked loops are analyzed for both ideal and additive white gaussian noise inputs. In addition, a design for a hardware digital phase locked loop capable of either first or second order operation is presented along with appropriate experimental data obtained from testing of the hardware loop. All parameters chosen for the analysis and the design of the digital phase locked loop are consistent with an application to an Omega navigation receiver although neither the analysis nor the design are limited to this application.
'Second-order quantizers' are introduced which can be used for implementing recursive digital filters with practically no roundoff errors or limit-cycle oscillations. Based on the idea of changing the transfer function used to compute roundoff errors, these quantizers save the low-order bits to correct the product at future iterations. For several pole locations, this can be done with a minimal amount of extra hardware.
This paper describes the design of an all digital FM discriminator. The system can be easily constructed using ordinary commercially available, digital IC's. In addition, the output SNR above threshold is computed. It is shown that the output noise consists of two terms: the first being the expected output gaussian noise having a parabolic power spectral density and the second being a quantization noise produced by the finite-level detection process used in the receiver.
The next era of space exploration, especially the "Mission to Planet Earth" will generate immense quantities of image data. For example, the Earth Observing System (EOS) is expected to generate in excess of one terabyte/day. NASA confronts a major technical challenge in managing this great flow of imagery: in collection, pre-processing, transmission to earth, archiving, and distribution to scientists at remote locations. Expected requirements in most of these areas clearly exceed current technology. Part of the solution to this problem lies in efficient image compression techniques. For much of this imagery, the ultimate consumer is the human eye. In this case image compression should be designed to match the visual capacities of the human observer. We have developed three techniques for optimizing image compression for the human viewer. The first consists of a formula, developed jointly with IBM and based on psychophysical measurements, that computes a DCT quantization matrix for any specified combination of viewing distance, display resolution, and display brightness. This DCT quantization matrix is used in most recent standards for digital image compression (JPEG, MPEG, CCITT H.261). The second technique optimizes the DCT quantization matrix for each individual image, based on the contents of the image. This is accomplished by means of a model of visual sensitivity to compression artifacts. The third technique extends the first two techniques to the realm of wavelet compression. Together these two techniques will allow systematic perceptual optimization of image compression in NASA imaging systems. Many of the image management challenges faced by NASA are mirrored in the field of telemedicine. Here too there are severe demands for transmission and archiving of large image databases, and the imagery is ultimately used primarily by human observers, such as radiologists. In this presentation I will describe some of our preliminary explorations of the applications of our technology to the special problems of telemedicine.
The amount of quantization noise generated in a digital-to-analog converter is dependent on the number of bits or quantization levels used to digitize the analog signal in the analog-to-digital converter. The minimum number of quantization levels and the minimum sample rate were derived for a digital voice channel. A sample rate of 6000 samples per second and lowpass filters with a 3 db cutoff of 2400 Hz are required for 100 percent sentence intelligibility. Consonant sounds are the first speech components to be degraded by quantization noise. A compression amplifier can be used to increase the weighting of the consonant sound amplitudes in the analog-to-digital converter. An expansion network must be installed at the output of the digital-to-analog converter to restore the original weighting of the consonant sounds. This technique results in 100 percent sentence intelligibility for a sample rate of 5000 samples per second, eight quantization levels, and lowpass filters with a 3 db cutoff of 2000 Hz.
Specifications for the pointing stabilization system of the large space telescope were used in an investigation of the feasibility of reducing ring laser gyro output quantization to the sub-arc-second level by the use of phase locked loops and associated electronics. Systems analysis procedures are discussed and a multioscillator laser gyro model is presented along with data on the oscillator noise. It is shown that a second order closed loop can meet the measurement noise requirements when the loop gain and time constant of the loop filter are appropriately chosen. The preliminary electrical design is discussed from the standpoint of circuit tradeoff considerations. Analog, digital, and hybrid designs are given and their applicability to the high resolution sensor is examined. the electrical design choice of a system configuration is detailed. The design and operation of the various modules is considered and system block diagrams are included. Phase 1 and 2 test results using the multioscillator laser gyro are included.
The suitability is explored of two varieties of distributed memory neutral networks as trainable controllers for a simulated robotics task. The task requires that two cameras observe an arbitrary target point in space. Coordinates of the target on the camera image planes are passed to a neural controller which must learn to solve the inverse kinematics of a manipulator with one revolute and two prismatic joints. Two new network designs are evaluated. The first, radial basis sparse distributed memory (RBSDM), approximates functional mappings as sums of multivariate gaussians centered around previously learned patterns. The second network types involved variations of Adaptive Vector Quantizers or Self Organizing Maps. In these networks, random N dimensional points are given local connectivities. They are then exposed to training patterns and readjust their locations based on a nearest neighbor rule. Both approaches are tested based on their ability to interpolate manipulator joint coordinates for simulated arm movement while simultaneously performing stereo fusion of the camera data. Comparisons are made with classical k-nearest neighbor pattern recognition techniques.