Showing papers on "Superposition principle published in 1991"

Atom- and field-state evolution in the Jaynes-Cummings model for large initial fields.

Abstract: An asymptotic result is derived for the Jaynes-Cummings model of a two-level atom interacting with a quantized single-mode field, which is valid when the field is initially in a coherent state with a large average photon number. It is shown that for certain initial atomic states the joint atom-field wave function factors into an atomic and a field part throughout the interaction, so that each system remains separately in a pure state. The atomic part of the wave function displays a crossing of trajectories in the atom Hilbert space that leads to a unique state for the atom, independent of its initial state, at a specific time to (equal to half the revival time). The field part of the wave function resembles a crescent squeezed state. The well-known collapses and revivals are investigated from this perspective. The collapse appears to be associated with a "measurement" of the initial state of the atom with the field as the measuring apparatus. The measurement is not complete for finite average photon number: the system is instead left in a coherent superposition of macroscopically distinct states. At the half-revival time to this superposition of states is entirely in the field part of the state vector, so that the (pure) state of the field at that time is of the form sometimes referred to as a "Schrodinger cat. " The revivals of the population inversion are seen to be entirely due to the fact that the linear superposition of the two macroscopically distinct field states is coherent (i.e., a pure state), as opposed to an incoherent mixture.

Loss performance analysis of an ATM multiplexer loaded with high-speed on-off sources

Abstract: The performance of an asynchronous transfer mode (ATM) multiplexer whose input consists of the superposition of a multiplicity of homogeneous on-off sources modeled by a two-state Markovian process is studied. The approach is based on the approximation of the actual input process by means of a suitably chosen two-state Markov modulated Poisson process (MMPP), as a simple and effective choice for the representation of superposition arrival streams. To evaluate the cell loss performance, a new matching procedure that leads to accurate results compared to simulation is developed. The application limits of the proposed method are also discussed. The outstanding physical meaning of this procedure permits a deep insight into the multiplexer performance behavior as the source parameters and the multiplexer buffer size are varied. >

Effects of high-numerical-aperture focusing on the state of polarization in optical and magneto-optic data storage systems.

Abstract: Using vector diffraction theory and an exact method for computing reflection coefficients for multilayer structures, we analyze the effects of high-numerical-aperture focusing on the state of polarization in optical data storage systems. The focused incident beam is decomposed into a spectrum of plane waves, and the reflected beam is obtained by the superposition of these plane waves after they are independently reflected from the multilayer. Plots of polarization rotation angle and ellipticity for several disk structures are presented.

Numerical errors associated with the method of superposition for computing acoustic fields

Abstract: The method of “wave superposition” is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources. The accuracy of this representation depends upon how well the velocity boundary condition on the surface of the body is approximated. The ultimate objective of this study, then, is to provide some guidelines for improving the accuracy of the surface velocity reconstruction and, consequently, the accuracy of the superposition solutions. In general, this is dependent upon the particular surface velocity distribution to be reconstructed, as well as other formulation factors such as the acoustic wave number, the number and locations of the surface nodes, and the number and locations of the point sources. Velocity interpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources. Numerical experiments on cylindrical radiators with different velocity distributions are performed to further illustrate how the solution accuracy depends on the surface velocity boundary conditions as well as the other formulation factors.

On the evolution of a wave packet in a laminar boundary layer

Abstract: The transition process of a small-amplitude wave packet, generated by a controlled short-duration air pulse, to the formation of a turbulent spot is traced experimentally in a laminar boundary layer. The vertical and spanwise structures of the flow field are mapped at several downstream locations. The measurements, which include all three velocity components, show three stages of transition. In the first stage, the wave packet can be treated as a superposition of two- and three-dimensional waves according to linear stability theory, and most of the energy is centred around a mode corresponding to the most amplified wave. In the second stage, most of the energy is transferred to oblique waves which are centred around a wave having half the frequency of the most amplified linear mode. During this stage, the amplitude of the wave packet increases from 0.5 % to 5 % of the free-stream velocity. In the final stage, a turbulent spot develops and the amplitude of the disturbance increases to 27 % of the free-stream velocity.Theoretical aspects of the various stages are considered. The amplitude and phase distributions of various modes of all three velocity components are compared with the solutions provided by linear stability theory. The agreement between the theoretical and measured distributions is very good during the first two stages of transition. Based on linear stability theory, it is shown that the two-dimensional mode of the streamwise velocity component is not necessarily the most energetic wave. While linear stability theory fails to predict the generation of the oblique waves in the second stage of transition, it is demonstrated that this stage appears to be governed by Craik-type subharmonic resonances.

A numerical solution for the general radiation problem based on the combined methods of superposition and singular‐value decomposition

Abstract: In the method of wave superposition, the acoustic field, due to a complex radiator, is expressed in terms of a Fredholm integral equation of the first kind called the ‘‘superposition integral equation.’’ In general, Fredholm integral equations of the first kind are ill‐posed and therefore difficult to solve numerically. In this paper, it will be shown that a simple collocation procedure, when combined with the singular‐value decomposition, can yield accurate results for the numerical solution of the superposition integral. As an example of the application of the method, the acoustic radiation from a circular cylinder will be analyzed using this numerical procedure and compared to the exact solution. It is shown that, for this problem, the accuracy of the numerical solution can be judged by evaluating how well the superposition solution approximates the specified boundary condition on the surface of the radiator. An example is also given of a problem which has no exact solution. In this situation, it is suggested, without proof, that the accuracy of the numerical solution can be judged in a similar manner by evaluating the error in the superposition solution’s satisfaction of the boundary condition.

Phase-space beam summation for time-dependent radiation from large apertures: continuous parameterization

Abstract: We extend the study of alternative phase-space formulations of time-harmonic radiation from extended but truncated aperture source distributions to the time domain. Included are nonwindowed continuous forms spanning the space–time (configuration) domains, wave-number-frequency (spectrum) domains, and windowed (local beam-type) continuous forms. Synthesized in the frequency domain by nonwindowed or windowed Fourier transforms, field synthesis in the time domain involves nonwindowed or windowed radon transforms combined with the theory of analytic signals. Because the properties of suitable wave objects used in the analysis and synthesis of the field are strongly tied to relevant configurational and spectral parameters, the incorporation of these aspects into the various formats is referred to as phase-space parameterization. In the continuous parameterization the resulting time-dependent field radiated from the aperture is expressed as a superposition of pulsed beams whose phase-space parameters are their initiation time, initiation location, and initial direction. The properties of these formulations are discussed in detail, within a rigorous format and also with more physically transparent asymptotic approximations. As in the time-harmonic case, major stress is placed on localization in the phase space, which is achievable with various alternatives, and on the corresponding implications. Specific examples include analytic δ windows that yield as propagators complex-source pulsed beams, and numerical implementation of field synthesis for nonfocused and focused pulsed aperture distributions.

Improved mode-superposition technique for modal frequency response analysis of coupled acoustic-structural systems

Abstract: A new formulation is derived by using an orthogonality condition of a coupled system. An improved compensation technique is then proposed for compensating for the effect of truncated modes, which are the lower and/or higher modes beyond the frequency domain of an MFR analysis

Dipole squeezing in the two-photon Jaynes-Cummings model with superposition state preparation

Abstract: Quantum fluctuations of atomic dipole variables in the two-photon Jaynes-Cummings model are discussed. It is shown that dipole squeezing can be exhibited in certain periods of time evolution of the system for superposition state preparations, and also that the dipole fluctuations cannot be squeezed in atomic spontaneous radiation processes.

Principle of superposition: a common computational framework for analysis of multiple motion

Abstract: The principle of superposition is applied to various motion estimation problems. It can potentially resolve the difficulty of analyzing multiple motion, transparent motion and motion boundaries by using a common mathematical structure. The authors demonstrate that, by applying the principle, the techniques of optical flow, 3D motion and structure from flow fields, direct method for 3D motion and structure recovery, motion and structure from correspondences in two frames can be extended coherently to deal with multiple motion. The theory not only produces multiple-motion versions of the existing algorithms, but also provides tools for the theoretical analysis of multiple motion. Since the approach is not at the algorithm level as are conventional segmentation paradigms, but at the level of computational theory, i.e. of constraints, theoretical results derived also contribute to psychophysical and physiological studies on the preattentive stages of biological motion vision systems. The paper emphasizes the universality of the principle. >

Transient and stationary distributions for fluid queues and input processes with a density

Abstract: Transient and stationary distributions of queue content for fluid queues whose continuous input process has a density with respect to time are studied. Results are obtained via a method primarily introduced by Benes, when considering input processes increasing by jumps at random times. The general formulas are applied to the queue where the input density varies as a stationary Ornstein-Uhlenbeck process. Such fluid queue models are useful in the field of telecommunications for dimensioning studies of packet multiplexers which are offered a superposition of variable bit rate video sources.

Discrete superpositions of coherent states and phase properties of elliptically polarized light propagating in a Kerr medium

Abstract: The problem of the formation of discrete superpositions of coherent states when elliptically polarized light is propagating through a nonlinear Kerr medium is considered, It is shown that superpositions with any number of components can be obtained if the evolution time is taken as a fraction MIN of the period, where M and N are mutually prime integers. Exact analytical formulae for finding the superposition coeffi- cients are given. It is shown that the coupling between the two circularly polarized components of the ellpitically polarized light caused by the asymmetry of the nonlinear properties of the medium can suppress the number of components in the superposition from N' to N, if the asymmetry parameter takes appropriate values. The phase distri- bution function P(.9,, e.) for the two-mode field is obtained according to the new Pegg-Barnett phase formalism. This function exhibits a well resolved, multi-peak struc- ture, clearly indicating the formation of the discrete superpositions of coherent states. Examples of the phase distribution function for several superposition states are illustrated graphiczlly. showing in a very spectacular way the formation of such superpositions.

A further test of the superposition model for the redundant-signals effect in bimodal detection.

Abstract: The superposition model proposed by Schwarz (1989) to account for the redundant-signals effect in a bimodal detection task with visual and auditory signals is tested further. It is shown that the model does not fit the observed standard deviations reported by Miller (1986) if the residual (motor) component is assumed to be independent of the waiting time.

Mechanism of the noise reduction method by superposition of high-frequency current for semiconductor injection lasers

Abstract: Semiconductor injection lasers sometimes reveal excess noise called the mode hopping noise, which is associated with the mode hopping phenomena among longitudinal modes. The mode hopping phenomena are caused by coupling effects among lasing modes. To reduce this kind of noise superposition of high-frequency (HF) current on the injection current is frequently used. This reduction method is theoretically analyzed based on the mode competition theory and is compared with experimental measurements. It is confirmed that the coupling effect among the longitudinal modes is released with the HF superposition because of enhanced vibration of the injected electron, resulting in reduction of the mode hopping noise. >

Twin-image elimination in in-line holography of finite-support complex objects.

Abstract: Reconstruction of in-line holograms suffers from the superposition of two twin images having different foci but identical information content. A simple iterative method of twin-image elimination is presented here. It is based on the fact that, if the object has a finite support and the recording distance is not too small, the out-of-focus field is known on a large part of the reconstruction plane and is only superposed by the in-focus one inside a restricted support. An iterative procedure is developed to recover the out-of-focus wave inside the in-focus image support. Inverse diffraction then gives the reconstructed image. This procedure can be easily auto-mated and works for finite-support real or complex objects, recorded in geometries with a Fresnel number of ~1.

Schrödinger equation for convex plane polygons: A tiling method for the derivation of eigenvalues and eigenfunctions

Abstract: Motivated by a recently advanced conjecture on the ergodic properties of Quantum Systems, the problem of solving the Schrodinger equation for a free particle in a plane polygonal enclosure is revisited. It will be shown that two elementary lemmas suffice to give a complete characterization of the polygons for which a solution can be found in terms of a finite superposition of plane waves, without making use of advanced group‐theoretical techniques. It turns out, inter alia, that these polygons, considered as classical billiards, are all and only those which are completely integrable in the sense of Arnold’s theorem.

Is a quantum standing wave composed of two traveling waves

Abstract: We compare the scattering of an atom by two different quantized standing-wave configurations The first one is established in a cavity by a pair of fixed mirrors The other consists of two independent counterpropagating traveling waves, as could occur in a ring configuration We show that in the quantum regime (of small photon numbers) atoms are scattered differently by a true standing wave than by a superposition of two counterpropagating waves of equal amplitudes and opposite directions This behavior is a manifestation of momentum conservation In the case of traveling waves each wave depletes its momentum independently, whereas the standing wave that is fixed in space acts as a potentially infinite sink or source for momentum

Some results on the Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Abstract: In this paper, a hierarchy of bilinear Caudrey-Dodd-Gibbon-Kotera-Sawada equations with a unified structure is proposed. A nonlinear superposition formula for the CDGKS equation is proved under certain conditions. A Backlund transformation for a higher-order CDGKS equation is presented.

Exact perturbation treatment of the basis set superposition correction

Abstract: It is shown that a complete removal of the basis set superposition effect on the interaction properties of a composite system can be understood in terms of constraints imposed on its wave function. This interpretation of the basis set superposition effect is used to build variation methods which account for the constraints imposed by the incompleteness of available solutions for the constituent subsystems. A perturbation analysis of the resulting constrained equations provides an exact method for the evaluation of the basis set superposition contribution to interaction properties. The corresponding perturbation correction is explicitly evaluated for the Hartree–Fock approximation and discussed at the level of different correlated methods.

Quantum state evolution of the fundamental mode in the process of second-harmonic generation

Abstract: By the computer calculations of the quasiprobability distribution the authors have shown that in a process of second-harmonic generation at phase matching conditions the quantum state of the fundamental mode evolves into a superposition of two macroscopically distinguishable states. Creation of the superposition destroys the squeezing formed in the initial stage of the evolution of the fundamental mode.

Superposition Refinement of Parallel Algorithms

Abstract: Superposition refinement enhances an algorithm by superposing one computation mechanism onto another mechanism, in a way that preserves the behavior of the original mechanism Superposition seems to be particularly well suited to the development of parallel and distributed programs An originally simple sequential algorithm can be extended with mechanisms that distribute control and state information to many processes, thus permitting efficient parallel execution of the algorithm We will in this paper show how superposition of parallel algorithms is expressed in the refinement calculus We illustrate the power of this method by a case study, showing how a distributed broadcasting algorithm is derived through a sequence of superposition refinements

A maximum likelihood detector for nonlinear magnetic recording

Abstract: Extremely high density magnetic recording is not well modeled by linear superposition. A model for nonlinearities in thick particulate media is described, and a simple maximum likelihood detector to this channel is derived. The authors first review the nonlinear recording model of A. Armstrong et al., (1991) and then describe the architecture of the maximum likelihood sequences estimator for the channel. It is observed that further simplifications to the detector can be made when the channel can be described in terms of partial response signals. Some simulation results obtained for a simple channel model are reviewed. >