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Based on the self-consistent phonon theory, the spectral energy density is calculated by the canonical transformation and the Fourier transformation. Through fitting the spectral energy density by the Lorentzian profile, the phonon frequency as well as the phonon relaxation time is obtained in one-dimensional nonlinear lattices, which is validated in the Fermi–Pasta–Ulam-β (FPU-β) and ϕ4 lattices at different temperatures. The phonon mean free path is then evaluated in terms of the phonon relaxation time and phonon group velocity. The results show that, in the FPU-β lattice, the phonon mean free path as well as the phonon relaxation time displays divergent power-law behavior. The divergent exponent coincides well with that derived from the Peierls–Boltzmann theory at weak anharmonic nonlinearity. The value of the divergent exponent expects a power-law divergent heat conductivity with system size, which violates Fourier's law. For the ϕ4 lattice, both the phonon relaxation time and mean free path are finite, which ensures normal heat conduction. [ABSTRACT FROM AUTHOR]

The Rayleigh–Taylor instability at the weakly nonlinear (WN) stage in spherical geometry is studied by numerical simulation. The mode coupling processes are revealed. The results are consistent with the WN model based on parameter expansion, while higher order effects are found to be non-negligible. For Legendre mode perturbation Pn(cosθ), the nonlinear saturation amplitude (NSA) of the fundamental mode decreases with the mode number n. When n is large, the spherical NSA is lower than the corresponding planar one. However, for large n, the planar NSA can be recovered by applying Fourier transformation to the bubble/spike near the equator and calculating the NSA of the converted trigonometric harmonic. [ABSTRACT FROM AUTHOR]

A coupled-mode method for three-dimensional acoustic propagation and scattering in two-dimensional waveguides is presented. This method synthesizes the three-dimensional field solution by using Fourier transform techniques based on a sequence of two-dimensional problems, each of which is solved by a numerical model recently developed by Luo et al. [Chin. Phys. Lett. 29 (2012) 014302]. Numerical results indicate that the present model is remarkably accurate, and thus can serve as benchmark against other numerical models. In addition, this model can be applied to realistic problems, and can also be used to analyze horizontal refraction in some range-dependent waveguides in reality, such as the continental shelf environment, ridge-like bathymetry, and underwater trenches. [ABSTRACT FROM AUTHOR]

We introduce a generalized joint density of states (GJDOS), which incorporates the coherent factors into the JDOS, to study quasiparticle interference (QPI) in superconductors. The intimate relation between the Fourier-transformed local density of states and GJDOS is revealed: they correspond respectively to the real and imaginary parts of a generalized impurity-response function, and particularly share the same angular factors and singular boundaries, as seen from our approximate analytic results for d-wave superconductors. Remarkably, our numerical GJDOS analysis agrees well with the QPI patten of d-wave cuprates and s±-wave iron-based superconductors. Moreover, we illustrate that the present GJDOS scenario can uncover the sign features of the superconducting gap and thus can be used to explore the pairing symmetry of the A1-xFe2-y Se2 (A=K,Cs, etc) superconductors. [ABSTRACT FROM AUTHOR]

A methodology is presented to obtain the basis of qudits which are admissible to quantum Fourier transform (QFT) in the sense that the set of such kets are related by the QFT in the same way as the kets of the computational basis. We first study this method for qubits to characterize the ensemble that works for the Hadamard transformation (QFT for two dimension). In this regard we identify certain incompleteness in the result of Maitra and Parashar (Int. J. Quantum Inform. 4 (2006) 653). Next we characterize the ensemble of qutrits for which QFT is possible. Further, some theoretical results related to higher dimensions are also discussed. Considering the unitary matrix n related to QFT, the issue boils down to the problem of characterizing matrices that commute with n [ABSTRACT FROM AUTHOR]

We investigate the Ramsey fringes of a single electron spin of the nitrogen-vacancy center in diamond with different microwave radiation frequency detunings. The fast Fourier transform demonstrates that the Ramsey fringes consist of three components caused by hyperfine interaction with 14 N nuclear spin, and the Ramsey fringes cannot be well explained without the phase term of the three components, which has not been mentioned before. Each phase is determined by the microwave frequency detuning and the resonant Rabi frequency as well as the π/2 pulse. [ABSTRACT FROM AUTHOR]

An analytical model of acoustic field excited by a pulsed-laser line source on a coated cylinder is presented. Surface wave dispersive behaviours for a cylinder with a slow coating are analysed and compared with that of a bare cylinder. Based on this analysis, the laser-generated transient response of the perturbed Rayleigh wave and the higher modes of steel cylinder with a zinc coating are calculated from the model using residue theory and FFT technique. The theoretical result from the superposed waveform of the perturbed Rayleigh wave and higher modes agree well with the waveform obtained in experiment. The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves. [ABSTRACT FROM AUTHOR]

Discretization of the Lippmann-Schwinger integral equation with complex conjugate gradient method and fast Fourier transform (CCGM-FFT) is solved, which can reduce the memory storage and the CPU time compared with the traditional method, MOM. Thus objects with large size and multiple scattering objects could be simulated with CCGM-FFT. The total intensity and the distribution of each field component of the dielectric and metallic objects under the excitation of the TE/TM-polarized wave are calculated with photon scanning tunnelling microscopy (PSTM) at the constant height. The simulating results are analysed and explained reasonably. The results show that the polarization plays an important role for imaging of PSTM. [ABSTRACT FROM AUTHOR]

We study the transport property passing through a weakly open equilateral triangular billiards by using the semiclassical method. We extend the Green function and the transport matrix theory to include the multiple scattering effect at the boundary and the diffractions of the pair of the lead apertures. For analysing the structure of semiclassical pseudo path kinks, the geometric and the special dynamical symmetries of the system are simultaneously taken into account. The conductance is calculated by Landauer formula as a function of the electron's Fermi wave number. Its Fourier transformation, the quantum path-length spectrum, is qualitatively in accordance with the results of the classical trajectories, which indicates that such approach provides an obvious improvement of the semiclassical description. [ABSTRACT FROM AUTHOR]

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched. [ABSTRACT FROM AUTHOR]

Two coupled parametric four-wave-mixing processes in Rb atoms are studied using perturbation theory, which reveals clear evidence of the appearance of quantum beat at 608 cm[?]1, corresponding to the energy difference of the 7s[?]5d states of Rb atoms, in the parametric four-wave-mixing signals. A pump-probe technique is utilized to observe the quantum beat. Time-varying characteristics of the quantum beat are investigated using time-dependent Fourier transform. The results show that the time-varying characteristics of the quantum beat not only offers a sensitive detecting method for observing the decay of atomic wave packets, but also provides a potential tool for monitoring the dissociation of molecules. [ABSTRACT FROM AUTHOR]

The photodetachment cross section of H[?] in parallel electric and magnetic fields near an elastic surface is derived and calculated by using the closed orbit theory. It is found that the elastic surface can produce some interesting effects. Besides the closed orbits previously found by Peters et al. for the H[?] in parallel electric and magnetic fields, some additional closed orbits are produced due to the effect of the elastic surface. The results show that the cross section oscillation is much more complicated in comparison with the cross section of H[?] in parallel external fields without surface. Each peak in the Fourier transformed cross section corresponds to the period of one detached electron closed orbit. This study provides a new understanding of the photodetachment of negative ions in the presence of external fields and surface. [ABSTRACT FROM AUTHOR]

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are ?2= 4.69and ?4= 4.6, which are comparable with the theoretical asymptotic value ? = 4.669. [ABSTRACT FROM AUTHOR]

A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra. [ABSTRACT FROM AUTHOR]

We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed. [ABSTRACT FROM AUTHOR]

We experimentally measure the sodium D-lines from the multibubble sonoluminescence in sodium hydroxide aqueous solution. The asymmetric overlapping D-lines are successfully decomposed based on the Fourier transform analysis. The line broadening of the decomposed sodium D-lines shows the effective temperature of 3600–4500 K and the pressure of 560–1000 atm during sonoluminescence. [ABSTRACT FROM AUTHOR]

Measurement-based one-way quantum computation, which uses cluster states as resources, provides an efficient model to perform computation. However, few of the continuous variable (CV) quantum algorithms and classical algorithms based on one-way quantum computation were proposed. In this work, we propose a method to implement the classical Hadamard transform algorithm utilizing the CV cluster state. Compared with classical computation, only half operations are required when it is operated in the one-way CV quantum computer. As an example, we present a concrete scheme of four-mode classical Hadamard transform algorithm with a four-partite CV cluster state. This method connects the quantum computer and the classical algorithms, which shows the feasibility of running classical algorithms in a quantum computer efficiently. [ABSTRACT FROM AUTHOR]

Realizing the logic operations with small-scale states is pursued to improve the utilization of quantum resources and to simplify the experimental setup. We propose a scheme to realize a general single-mode Gaussian operation with a two-mode entangled state by utilizing only one nondegenerate optical parametric amplifier and by adjusting four angle parameters. The fidelity of the output mode can be optimized by changing one of the angle parameters. This scheme would be utilized as a basic efficient element in the future large-scale quantum computation. [ABSTRACT FROM AUTHOR]

We investigate the structure-preserving numerical algorithm of the Degasperis—Procesi equation which can be transformed into a bi-Hamiltonian form using the discrete variational derivative method. Based on two different space discretization methods, the Fourier pseudospectral method and the wavelet collocation method, we develop two modified structure-preserving schemes under the periodic boundary condition. These proposed schemes are proved to preserve the Hamiltonian invariants theoretically and numerically. Meanwhile, the numerical results confirm that they can simulate the propagation of solitons effectively for a long time. [ABSTRACT FROM AUTHOR]

Based on Dirac's representation theory and the technique of integration within an ordered product of operators, we put forward the joint wavelet—fractional Fourier transform in the context of quantum mechanics. Its corresponding transformation operator is found and the normally ordered form is deduced. This kind of transformation may be applied to analyzing and identifying quantum states. [ABSTRACT FROM AUTHOR]

The retrieval of ptychographical imaging encounters a degradation produced by motion of samples. The mechanism of capturing the diffractive patterns of a sample which is motile is simulated numerically. The relation between the retrieval degradation and the amplitude of motion is evaluated quantitatively. Experiments indicate that the reliability and resolution of the complex amplitude retrieval of a sample is inversely proportional to its vibratory amplitude. A random phase modulated aperture is employed to cure the degradation produced by the motion of samples to a certain extent. [ABSTRACT FROM AUTHOR]

An alternative extension to the Gaussian-beam expansion technique is provided to simplify the computation of the Fresnel field integral for rectangular symmetric sources. From a known result that the circle or rectangle function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel–Fourier transform. Two expansions are together inserted in this field integral, it is then expressible in terms of the simple algebraic functions. As examples, the numerical results for the sound pressure field are presented for the uniform rectangular piston transducer, in a good agreement with those directly evaluated from the Fresnel integral. A wide applicability of this approach is discussed in treatment of the ultrasonic field radiation problem for a large and important group of piston sources in acoustics. [ABSTRACT FROM AUTHOR]

We report a heptad vortex array structure in the wave fields in an extremely deep Fresnel diffraction region by asymmetrical subwavelength holes in a metal film illuminated with linearly polarized light. A Mach–Zehnder interferometer with a microscopic objective is used to record the wave fields at different distances, and the phase maps are extracted by Fourier transform of the interference intensities. We study the evolutions of the heptad vortex array with distance from the sample to the object plane. To explain the formations and the evolutions of the vortex array, we calculate the diffracted wave fields with Kirchhoff's diffraction theory. The calculations are basically consistent with the experimental results, and the properties of the heptad vortex array structure are reasonably explained. [ABSTRACT FROM AUTHOR]

We propose and implement a wide-field vibrational phase contrast detection to obtain imaging of imaginary components of third-order nonlinear susceptibility in a coherent anti-Stokes Raman scattering (CARS) microscope with full suppression of the non-resonant background. This technique is based on the unique ability of recovering the phase of the generated CARS signal based on holographic recording. By capturing the phase distributions of the generated CARS field from the sample and from the environment under resonant illumination, we demonstrate the retrieval of imaginary components in the CARS microscope and achieve background free coherent Raman imaging. [ABSTRACT FROM AUTHOR]

Considering the inclusive process, we study the doubly heavy baryon Ξcc (Ξbb) production through e+e− annihilation. Both the diquark QQ in color sextet and triplet are discussed. The results show that the contributions from these two color states play equally important roles. At the Z0 pole, a significant enhancement can be found in the doubly heavy baryon production. [ABSTRACT FROM AUTHOR]

A dissipation rate, which grows faster than any power of the wave number in Fourier space, may be scaled to lead a hydrodynamic system to actually or potentially converge to its Galerkin truncation. Actual convergence here means the asymptotic truncation at a finite wavenumber kG above which modes have no dynamics; and, we define potential convergence for the truncation at kG which, however, grows without bound. Both types of convergence can be obtained with the dissipation rate m[cosh(k/kc) [?]1] that behaves as k2 (newtonian) and exp{k/kc} for small and large k/kc respectively. Competing physics of cascade, thermalization and dissipation are discussed for numerical Navier-Stokes turbulence, emphasizing the intermittency growth issue. [ABSTRACT FROM AUTHOR]

Modulated supersonic molecular beam (SMB) injection is introduced to study transport features of non-local transport phenomenon on HL-2A. Repetitive non-local effect induced by modulated SMBI allows Fourier transformation of the temperature perturbation, yielding detailed investigation of the pulse propagation. Fourier analysis provides evidence for existence of internal transport barriers. Meanwhile, experimental progress of nonlocal effect was made in the HL-2A Tokamak in 2007. The core electron temperature Te rise increases from 18% to more than 40% and the duration of the Te rise could be prolonged by changing the conditions of SMB injection. [ABSTRACT FROM AUTHOR]

A novel three-dimensional wide-angle beam propagation method based on the split-step fast Fourier transform is developed. The formulation is based on the three-dimensional Helmholtz wave equation. Each propagation step is performed by utilizing both the FFT and split-step scheme. The solution of Helmholtz wave equation does not make the slowly varying envelope and one-way propagation approximations. To validate the efficiency and accuracy, numerical results for a propagation beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms. [ABSTRACT FROM AUTHOR]