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Showing papers on "Superposition principle published in 2001"


Journal ArticleDOI
TL;DR: It is proved that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l/sup 1/ norm of the coefficients among all decompositions.
Abstract: Suppose a discrete-time signal S(t), 0/spl les/t

2,207 citations


Book ChapterDOI
01 Jan 2001

208 citations


Journal ArticleDOI
TL;DR: In this article, nonequilibrium dynamics in Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetization, using specific cooling protocols before recording the thermo- or isothermal Remanent magnetizations on reheating, and it is found that the measured curves effectively disclose none-ilibrium spin glass characteristics such as aging and memory phenomena as well as an extended validity of the superposition principle for the relaxation.
Abstract: Nonequilibrium dynamics in a Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetization. Using specific cooling protocols before recording the thermo- or isothermal remanent magnetizations on reheating, it is found that the measured curves effectively disclose nonequilibrium spin glass characteristics such as aging and memory phenomena as well as an extended validity of the superposition principle for the relaxation. The usefulness of this ``simple'' dc method is discussed, as well as its applicability to other disordered magnetic systems.

128 citations


Journal ArticleDOI
TL;DR: In this paper, a realizable experimental scheme to prepare superposition of the vacuum and one-photon states by truncating an input coherent state was proposed, based on the quantum scissors device proposed by Pegg, Phillips and Barnett.
Abstract: We propose a realizable experimental scheme to prepare superposition of the vacuum and one-photon states by truncating an input coherent state. The scheme is based on the quantum scissors device proposed by Pegg, Phillips, and Barnett @Phys. Rev. Lett. 81, 1604 ~1998!# and uses photon-counting detectors, a single photon source, and linear optical elements. Realistic features of the photon counting and single-photon generation are taken into account and possible error sources are discussed together with their effect on the fidelity and efficiency of the truncation process. Wigner function and phase distribution of the generated states are given and discussed for the evaluation of the proposed scheme.

79 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered a system of two superconducting islands, each of which is coupled to a bulk superconductor via Josephson tunneling, and they considered a coherent superposition of two distinct quantum states in the large island.
Abstract: We consider a system of two superconducting islands, each of which is coupled to a bulk superconductor via Josephson tunneling. One of the islands represents a ``Cooper-pair box,'' i.e., it is an effective two-level system. The other island has a smaller charging energy and approximates a harmonic oscillator. A capacitive interaction between the islands results in a dependence of the oscillator frequency on the quantum state of the box. Placing the latter in a coherent superposition of its eigenstates and exciting coherent oscillations in the large island will lead to a phase shift of these oscillations depending on the box quantum state, thereby producing a coherent superposition of two ``mesoscopically distinct'' quantum states in the large island.

77 citations


Journal ArticleDOI
TL;DR: The algorithm for decoding a quantum state prepared in a superposition of states belonging to different irreducible representations of the rotation group is presented, and the fidelity of transmission is evaluated.
Abstract: A single quantum system, such as a hydrogen atom, can transmit a Cartesian coordinate frame (three axes). For this it has to be prepared in a superposition of states belonging to different irreducible representations of the rotation group. The algorithm for decoding such a state is presented, and the fidelity of transmission is evaluated.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the cross-polarization interaction between two intense counter-propagating laser beams in an isotropic optical fiber may lead to spatiotemporal polarization instabilities of both waves.
Abstract: The nonlinear interaction between two intense counterpropagating laser beams in an isotropic optical fiber may lead to spatiotemporal polarization instabilities of both waves. Experiments with various mutual polarization arrangements and different powers of the two counterpropagating input beams showed that nonlinear birefringence may lead to significant polarization cross switching of both beams. In the case of two counterrotating circular input waves, the cross-polarization interaction of the beams led to the generation of a polarization kink or domain wall soliton. This soliton is formed by a superposition of counterpropagating waves that represent switching of the state of polarization of light between two domains where both waves are circularly polarized and corotating. The experimental observations are found to be in good agreement with the theoretical predictions.

68 citations


Journal ArticleDOI
TL;DR: In this article, the problem of differential equation systems admitting a nonlinear superposition principle is analyzed from a geometric perspective, and it is shown how it is possible to reduce the general solution of such a differential equation system defined by a Lie group to a pair of simpler problems, one in a subgroup H and another on a homogeneous space.
Abstract: The problem of differential equation systems admitting a nonlinear superposition principle is analyzed from a geometric perspective. We show how it is possible to reduce the problem of finding the general solution of such a differential equation system defined by a Lie group G to a pair of simpler problems, one in a subgroup H and the other on a homogeneous space. The theory is illustrated with several examples and applications.

68 citations


Posted Content
TL;DR: In this paper, it was shown that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on a quantum computer, whereas the known fast algorithms on a classical computer need O(N log N).
Abstract: A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on a quantum computer, whereas the known fast algorithms on a classical computer need O(N log N) operations.

64 citations


Journal ArticleDOI
TL;DR: In this article, parallel superposition moduli on associative polymers are compared with superposition experiments in which the oscillatory motion is perpendicular to the steady-state flow, which has drastic consequences for the results.
Abstract: Oscillations superimposed on steady shear flows have been used repeatedly in the past to determine the relaxation modes in flowing associative polymers. In these experiments, the oscillatory motion has been parallel to the steady-state flow. Here, parallel superposition moduli on associative polymers will be compared with superposition experiments in which the oscillatory motion is perpendicular to the steady-state flow. In the latter experiments, there is less interference between the steady flow and the superimposed oscillations, which has drastic consequences for the results. Data are shown for a HASE polymer (hydrophobic alkali-swellable emulsion). As in other fluids, the limiting viscosities at zero frequency differ drastically, and negative storage moduli can be obtained in parallel superposition. The apparent relaxation frequencies during flow, as derived from parallel superposition measurements, are an order of magnitude smaller than those derived from orthogonal superposition. The effect of shear...

52 citations


Book ChapterDOI
01 Jun 2001
TL;DR: The double-slit experiment as mentioned in this paper is the quintessential experiment on quantum superposition, and has been performed with many different kinds of particles ranging from photons, via electrons, to neutrons, and atoms.
Abstract: The superposition principle plays the most central role in all considerations of quantum information, and in most of the “gedanken” experiments and even the paradoxes of quantum mechanics. Instead of studying it theoretically or defining it abstractly, we will discuss here the quintessential experiment on quantum superposition, the double-slit experiment (Fig. 1.1). According to Feynman [1], the double-slit “has in it the heart of quantum mechanics”. The essential ingredients of the experiment are a source, a double-slit assembly, and an observation screen on which we observe interference fringes. These interference fringes may easily be understood on the basis of assuming a wave property of the particles emerging from the source. It might be mentioned here that the double-slit experiment has been performed with many different kinds of particles ranging from photons [2], via electrons [3], to neutrons [4] and atoms [5].

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of the meaning of quantum unstable states including their dressing, and showed that quantum transitions are the result of two processes: a dressing process, discussed in a previous publication, and a decay process, which is much slower for electrodynamic systems.
Abstract: We consider the problem of the meaning of quantum unstable states including their dressing. According to both Dirac and Heitler this problem has not been solved in the usual formulation of quantum mechanics. A precise definition of excited states is still needed to describe quantum transitions. We use our formulation given in terms of density matrices outside the Hilbert space. We obtain a dressed unstable state for the Friedrichs model, which is the simplest model that incorporates both bare and dressed quantum states. The excited unstable state is derived from the stable states through analytic continuation. It is given by an irreducible density matrix with broken time symmetry. It can be expressed by a superposition of Gamow density operators. The main difference from previous studies is that excited states are not factorizable into wave functions. The dressed unstable state satisfies all the criteria that we can expect: it has a real average energy and a nonvanishing trace. The average energy differs from Green's function energy by a small effect starting with fourth order in the coupling constant. Our state decays following a Markovian equation. There are no deviations from exponential decay neither for short nor for long times, as ismore » the case for the bare state. The dressed state satisfies an uncertainty relation between energy and lifetime. We can also define dressed photon states and describe how the energy of the excited state is transmitted to the photons. There is another very important aspect: deviations from exponential decay would be in contradiction with indiscernibility as one could define, e.g., old mesons and young mesons according to their lifetime. This problem is solved by showing that quantum transitions are the result of two processes: a dressing process, discussed in a previous publication, and a decay process, which is much slower for electrodynamic systems. During the dressing process the unstable state is prepared. Then the dressed state decays in a purely exponential way. In the Hilbert space the two processes are not separated. Therefore it is not astonishing that we obtain for the unstable dressed state an irreducible density matrix outside the Liouville-Hilbert-space. This is a limit of Hilbert space states that are arbitrarily close to the decaying state. There are experiments that could verify our proposal. A typical one would be the study of the line shape, which is due to the superposition of the short-time process and the long-time process. The long-time process taken separately leads to a much sharper line shape, and avoids the divergence of the fluctuation predicted by the Lorentz line shape.« less

Journal ArticleDOI
TL;DR: It is demonstrated in this paper how the free field response can alternatively be computed, using the dynamic reciprocity theorem, applied to moving loads, based on the response of the soil due to the moving load distribution for a single axle load.
Abstract: In Krylov's analytical prediction model, the free field vibration response during the passage of a train is written as the superposition of the effect of all sleeper forces, using Lamb's approximate solution for the Green's function of a halfspace. When this formulation is extended with the Green's functions of a layered soil, considerable computational effort is required if these Green's functions are needed in a wide range of source-receiver distances and frequencies. It is demonstrated in this paper how the free field response can alternatively be computed, using the dynamic reciprocity theorem, applied to moving loads. The formulation is based on the response of the soil due to the moving load distribution for a single axle load. The equations are written in the wave-number-frequency domain, accounting for the invariance of the geometry in the direction of the track. The approach allows for a very efficient calculation of the free field vibration response, distinguishing the quasistatic contribution from the effect of the sleeper passage frequency and its higher harmonics. The methodology is validated by means of in situ vibration measurements during the passage of a Thalys high-speed train on the track between Brussels and Paris. It is shown that the model has good predictive capabilities in the near field at low and high frequencies, but underestimates the response in the midfrequency band.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear generalization of the diffusion-like operator found in linear theory is presented, whereby the diffusion operator is now a function of the density itself, which implies that the largest amplitude structures in the medium should be rotated away from zero flow angle conditions by a measurable amount.
Abstract: In the study of E region irregularities the standard procedure is to Fourier analyze the irregularities in both time and space, that is, to describe them as a superposition of plane waves. This introduces difficulties when the amplitude of the plane waves becomes large, thereby adding nonlinear terms to the original equations and forcing all the plane waves to become coupled to one another. In the present work we stay away from Fourier analysis and use the standard fluid description of the instabilities in the limit of perturbed electric fields that are strictly perpendicular to the geomagnetic field. We obtain a nonlinear generalization of the standard results whereby the diffusion-like operator found in linear theory is now a function of the density itself. Therefore, as the structures grow, the net electric field seen by the ambient plasma inside the structures changes in time: it rotates and its amplitude decreases. Consequently, one possible saturation mechanism for the instabilities is a reduction in the net electric field inside the structures, which brings them to threshold velocity conditions. This being stated, other nonlinear saturation mechanisms remain possible if they require smaller saturation amplitudes than the present work. Either way, our work is consistent with intermittency and implies that the largest amplitude structures in the medium should be rotated away from zero flow angle conditions by a measurable amount. Finally, we show that when compared to an irregularity-free situation, there should be a measurable reduction in the average Hall current carried by the plasma, while the average Pederseri current should not be affected.

Journal ArticleDOI
TL;DR: In this paper, an arbitrary density matrix is written as a superposition of gaussian pure states and the Hartree approximation is applied to each member of such an ensemble for homogeneous initial conditions.
Abstract: For homogeneous initial conditions, Hartree (gaussian) dynamical approximations are known to have problems with thermalization, because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a superposition of gaussian pure states and applying the Hartree approximation to each member of such an ensemble. Particles can then scatter via their back-reaction on the typically inhomogeneous mean fields. Starting from initial states which are far from equilibrium we numerically compute the time evolution of particle distribution functions and observe that they indeed display approximate thermalization on intermediate time scales by approaching a Bose-Einstein form. However, for very large times the distributions drift towards classical-like equipartition.

Journal ArticleDOI
TL;DR: In this paper, an alternative way to prepare arbitrary truncated states is presented, where a coherent state is previously injected into the cavity and the Wigner distribution function is sculptured, through atom-field interaction, from that representing the initial coherent state, the atoms playing the role of quantum chisels.
Abstract: Several interesting states of the quantized electromagnetic field are studied nowadays. Among them one can cite the number and ~its complementary! phase states @1#, the coherent @2# and squeezed states @3#, superposition states having the previous basic states as components @4#, the interpolating states @5#, which vary between two limiting states, going from one to the other, etc. So, in view of the existence of an abundance of states in quantum optics, it is of interest to know how to prepare these states experimentally, this procedure being known in the literature as ‘‘quantum state engineering’’ @6#. The engineering schemes may consider either the case of stationary waves prepared inside a ~high-Q) cavity @6,7# or the case of traveling waves @8,9#. In the realm of cavity QED phenomena, Vogel et al. @6# employed a resonant atom-field interaction to build up a trapped field in an initially empty cavity, while the proposal in Ref. @10# considers both resonant and dispersive atom-field interactions for the preparation of a general superposition in the empty cavity. An alternative proposal has been presented @11#, named the sculpture of quantum states, where a coherent state is previously injected into the cavity and the Wigner distribution function of the desired state is sculptured, through atom-field interaction, from that representing the initial coherent state, the atoms playing the role of quantum chisels. In recent work by Pegg, Phillips, and Barnett @8#, preparation of an arbitrary running-wave superposition of the vacuum and one-photon states, C0u0&1C1u1&, without using cavities was demonstrated. In this way, a traveling field would be available for further applications, including performing measurements on other field states @12,13#. The scheme in @8# obtains the above mentioned superposition by physical truncation of the photon number superposition making up a coherent state. The proposal requires no additional extension of current experiments and is reasonably insensitive to photodetection efficiency for the fields most likely to be used in practice. Since the scheme works via a truncation of the Hilbert space, it has been called a ‘‘quantum scissors’’ device @8#. As mentioned in @8#, states including superpositions of higher photon numbers might be fabricated by superposing fields prepared as superpositions of zeroand onephoton number states @14#. In this connection, we will present here an alternative way to prepare arbitrary truncated states, i.e., C0u0&1C1u1&1C2u2&1•••1CNuN&, N 51,2,3, . . . . . The method is a direct extension of that in @8#, called the optical truncation of a state by projection synthesis.

Journal ArticleDOI
TL;DR: In this paper, the authors derived all the required Boussinesq-Cerruti equations for constant, linear and bilinear distributions of normal and tangential load over a triangle area, and presented a solution set to the equations.
Abstract: Starting from the elastic solution to a concentrated load on an elastic half space, this paper derives all the required Boussinesq–Cerruti equations for constant, linear and bilinear distributions of normal and tangential load over a triangle area, and presents a solution set to the equations. The surface displacement field in both the normal and tangential direction is obtained. The evaluations of Boussinesq–Cerruti equations are achieved by using various integration techniques. This paper also suggests a composition methodology to construct the solution due to more complicated loading profiles using the principle of superposition.

Journal ArticleDOI
TL;DR: In this article, the propagation of Hermite-Gauss beams of any order along the optical axis of a uniaxially anisotropic crystal is investigated, and closed-form expressions of the electromagnetic field are given for this fundamental class of beams.
Abstract: Propagation of Hermite-Gauss beams of any order along the optical axis of a uniaxially anisotropic crystal is investigated. Starting from a general approach for solving boundary value problems in anisotropic materials, closed-form expressions of the electromagnetic field are given for this fundamental class of beams. Any optical beam in an anisotropic crystal is the superposition of ordinary and extraordinary parts, propagating independently. By analyzing the expressions of the fields originated by an input Gaussian beam, the effects of the anisotropy on the diffraction properties of the ordinary and extraordinary beams have been elucidated.

Journal ArticleDOI
TL;DR: In this paper, an explicit asymptotic theory for the lowest-loss mode, in terms of a superposition of successively magnified edge waves, was constructed for unstable lasers.


Journal ArticleDOI
TL;DR: Using the property that both the real and imaginary parts of the wave function are random Gaussian fields, the correlation function and densities of the nodal points are analyzed and the distribution of nearest neighbor separations is derived.
Abstract: According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from numerical calculations for the Berry wave function.

Patent
21 Aug 2001
TL;DR: In this paper, an interferometer system for splitting a beam emitted from the radiation source into a first partial beam and a second partial beam, and for subsequent superposition of the two partial beams, wherein optical path lengths of two partial beam differ by a predetermined length difference (d 1 ) between splitting and superposition, which length difference is greater than the coherence length.
Abstract: An interferometer system is disclosed. The system includes a radiation source for emitting radiation of a predetermined coherence length. The system also includes a device for splitting a beam emitted from the radiation source into a first partial beam and a second partial beam, and for subsequent superposition of the two partial beams, wherein optical path lengths of the two partial beams differ by a predetermined length difference (d 1 ) between splitting and superposition, which length difference is greater than the coherence length. The system also includes a beam transmitting arrangement for directing the superimposed partial beams towards two optically effective, especially partially reflecting structures which are disposed at a distance (d 2 ) from each other, wherein a first of the two structures is provided by the beam transmitting arrangement.

Journal ArticleDOI
TL;DR: In this paper, a pair of integral equations of the first kind which hold independently of the boundary conditions are constructed in the far-field region and the support of the body is found by noting that the solutions of the integral equations are not bounded as the point of the location of the fundamental solution approaches the boundary of the scatterer from interioir points.
Abstract: In this paper the far-field equations in linear elasticity for the rigid body and the cavity are considered. The direct scattering problem is formulated as a dyadic one. This imbedding of the vector problem for the displacement field into a dyadic field is enforced by the dyadic nature of the free space Green's function. Assuming that the incident field is produced by a superposition of plane dyadic incident waves it is proved that the scattered field is also expressed as the superposition of the corresponding scattered fields. A pair of integral equations of the first kind which hold independently of the boundary conditions are constructed in the far-field region. The properties of the Herglotz functions are used to derive solvability conditions and to build approximate far-field equations. Having this theoretical framework, approximate far-field equations are derived for a specific incidence which generates as far-field patterns simple known functions. An inversion scheme is proposed based on the unboundedness for the solutions of these approximate “far-field equations” and the support of the body is found by noting that the solutions of the integral equations are not bounded as the point of the location of the fundamental solution approaches the boundary of the scatterer from interioir points. It is also pointed that it is sufficient to recover the support of the body if only one approximate “far-field equation” is used. The case of the rigid sphere is considered to illuminate the unboundedness property on the boundary.

Journal ArticleDOI
TL;DR: In this article, the oblique interaction of internal solitary waves in a two-layer fluid system with infinite depth is studied, and the strong interactions of the non-linear long waves whose propagation directions are very close to each other are investigated.

Journal ArticleDOI
TL;DR: In this paper, a new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional reduction of the anti-self-dual Yang-Mills equations, is presented.
Abstract: A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional reduction of the anti-self-dual Yang–Mills equations, is presented. It represents a generalization of the Ernst–Weyl equation of General Relativity related to colliding neutrino and gravitational waves, as well as of the fourth order equation of Schwarzian type related to the KdV hierarchies, which was introduced by Nijhoff, Hone, and Joshi recently. An auto-Backlund transformation of the new system is constructed, leading to a superposition principle remarkably similar to the one connecting four solutions of the KdV equation. At the level of the Ernst–Weyl equation, this Backlund transformation and the associated superposition principle yield directly a generalization of the single and double Harrison transformations of the Ernst equation, respectively. The very method of construction also allows for revealing, in an essentially algorithmic fashion, other integrability features of the main subsystems, such as their reduction to the Painleve transcendents.

Journal ArticleDOI
TL;DR: In this article, the scalar stop hysteron model has the property of equal vertical chords for back-and-forth input variations of the same amplitude, which leads to an identification method of scalar model.
Abstract: The present paper first shows that the scalar stop hysteron model has the property of equal vertical chords for back-and-forth input variations of the same amplitude. This property leads to an identification method of the scalar model. Secondly, identification methods are developed for the 3-D and 2-D isotropic vector models that are constructed by the superposition of scalar stop hysteron models. Numerical simulations show that these methods identify the scalar and vector models satisfactorily.

Journal ArticleDOI
TL;DR: In this article, a simple method for creating a maximal coherent superposition of N states (a superposition state with equal amplitudes) in a robust way was presented, where the robustness of the population transfer out of a single state to the superposition is equivalent to stimulated Raman adiabatic passage.
Abstract: We present a simple method for creating a maximal coherent superposition of N states (a superposition state with equal amplitudes) in a robust way. We show that in the adiabatic limit the robustness of the population transfer out of a single state to the superposition state is equivalent to stimulated Raman adiabatic passage. As is typical for schemes based upon population trapping the method is insensitive to radiative decay from excited states.

Journal ArticleDOI
TL;DR: Photoassociation enables coherent intraparticle conversion, and it is proposed that this enables a viable scheme for creating a superposition of a macroscopic number of atoms with a macro scoping number of molecules.
Abstract: We theoretically examine photoassociation of a nonideal Bose-Einstein condensate, focusing on evidence for a macroscopic superposition of atoms and molecules. This problem raises an interest because, rather than two states of a given object, an atom-molecule system is a seemingly impossible macroscopic superposition of different objects. Nevertheless, photoassociation enables coherent intraparticle conversion, and we thereby propose a viable scheme for creating a superposition of a macroscopic number of atoms with a macroscopic number of molecules.

Journal ArticleDOI
TL;DR: From exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component, which gives a change in polarization that can be utilized to determine the properties of the biaxial medium.
Abstract: Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.

Journal ArticleDOI
01 Jun 2001-EPL
TL;DR: In this article, the dissipative dynamics of deformed coherent states superposition was studied and it was shown that such a kind of superposition can be more robust against decoherence than the usual Schrodinger cat states.
Abstract: We study the dissipative dynamics of deformed coherent states superposition. We find that such a kind of superposition can be more robust against decoherence than the usual Schrodinger cat states.